when you gain the names of power virtue, how many names do you know?
I dont see anything listed as far as number of names known but it seem s to say you only know some.
My thought was to link it to an ability such as magic or infernal lore, so you may know a numer of names per ability point, but how many is a good number?
Or is the original intent that you must quest for each name that you want access too?
none - when you are Initiated into the Mystery (ie gain the Virtue) you gain the method, but the rest is up to you
Further Questing is not needed - re-read the text in TMRE:
Each name is defined in game-terms as a Muto Vim spell - TMRE p.76 col.2
Only a magus with the Names of Power Virtue can use or learn such a spell, and even they can only use it to boost specific activities (each requiring further Virtues) - it is not designed to be any use as a free-standing power.
Note that this is a deliberate bit of over-simplification to get a usable game mechanic...
The troupe/storyguide need to work with the player to define the scope of
specific Names - a name eg "Jupiter" has a similar to Shape & Material Bonus values. A great name, like Jupiter, may offer several bonuses, and offer higher magnitude bonuses than a lesser name ("the Faerie Tempestus").
(Typically you don't work out a long list, but start with what the player is looking for ...)
In-character (rather than in game terms), the Great Names have many aspects and subtle nuances, above and beyond the basic sound of the name. It is not "J u p i t e r", but "Jupiter whose House is today Ascendant in the Sign of Aries" (and other mystical correspondences).
All magi know the basics of these correspondences, but mainly so as to control and restrain their magic so that it is well-behaved and consistent - Those with this virtue know how to interpret the nuances and mix them with other magic to gain advantage.
So, for instance, the troupe might agree that Jupiter offers bonuses on Lightning, Shapechange to Animal, and Lust. Since he's a Great Name, let's suggest Lightning +5, Shapechange to Animal +4, Lust +3.
So, a Personal Momentary Individual "Jupiter's Name as Lightning" spell is Lvl 25l. You could also consider a Lvl 30 spell providing a Diameter bonus.
(Personal/Ind are effectively fixed, with no useful variants; but you can vary the Duration to get a bonus for longer.)
If you have an extended duration, you can use the name for longer (typically, use it multiple times with one casting), but this is normally independent of the spell you boost - it's the casting process which is boosted.
If you know JNaL, and also know Names of Power and Hermetic Theurgy, you can invent Theurgy Invoke spells relating to Lightning, and add +5 (Jupiter's Lightning bonus) to your Lab Total and when you cast it, add +5 to casting Score. (Limited to a bonus of no more than your Magic Theory score).
If you do that, you have to speak your Invoke spell firmly, and state (or shout) Jupiter's name so it can be clearly heard all around. (And let any anti-pagans jump on you...)
In this case, you never actually cast the Jupiter Name spell....
If you have the Virtues Names Of Power and Invocation Magic instead (or as well) as Hermetic Theurgy, you can use Jupiter's Name as Lightning as an actual MuVi meta-magic spell. Cast it first, to boost your Casting Score, then during the Duration (or immediately for Mom duration), cast another spell with boosted Casting Score. Because it boosts your Casting Score, you can use it with Spont Magic, unlike other MuVi spells. You can't be silent - as above, you must speak firmly or shout so Jupiter's name can be heard. It takes the normal time (1 round for most magi) to cast the Name of power spell before the boosted spell. If you want to add several stacked bonuses (to limit of Magic Theory) you cast each in turn (1 r each).
If instead you have Names of Power and Consummate Talisman, you can invest Jupiter's name As Lightning as a MuVi device effect. (Like other device effects, you don't need to know a spell for this, but a Lab Text will help - but yet again it has to be a Names of Power Lab Text). Your Talisman can affect you with Range Personal Effects, so you can include Personal Mom Ind MuVi Names. These effects have a required trigger of "speak the name firmly or shout it" (same as the spells), as you not only trigger the magic in the device, but draw Jupiter's attention, too.
As noted in TMRE (and the online errata) you can combine multiple Names of power, and can combine names used via Theurgy, Invocation Magic and Consummate talisman - but the combined total bonus is limited by your Magic Theory score.
thanks.
I was thinking that if you knew one great name, then one spell could be used to give a WIDE range of bonuses which seemed very overpowering. I see now that you would need a different spell for each aspect of the name.
would a name dealing with fire give the bonus to all ignum spells, or only similar spells?
Would you use the same name for pillum of fire and BoF? would that also work for prison of flames or burst of flames? How restricted is a name?
you apply the same criteria to decide as with Shape & Material Bonus for enchantment (and the same kind of judgement as made for Magical Affinity and Puissant Magic).
The TMRE sections make it clear that Names of Power have similar qualities to the S&M bonuses - so go read up the core rules section on S&M, in the enchantments chapter. Also look over the lists of S&M bonuses in core 5e, and various supplements including TMRE itself.
Categories:
Ignem is a hugely wide category, including light (and darkness), heat (and cold) as well as fire. Very few names would have an Ignem bonus (though I note there are some S&M that do.)
Fire is quite broad, including extinguished fires.
Flame is more restrictive still, including only phenomena with actual live flames involved.
Generally weaker names are narrower in scope, and/or smaller in bonus. And, the wider a scope the smaller the bonus in general. Don't expect a Form or Technique bonus to exceed (say) +3.
How restricted is a name?
Work it out with the rest of the troupe - but remember
a) you can stack multiple Names which have overlapping bonus
b) no matter how you get the bonuses (multiple Names, or multiple Virtues (Hermetic Theurgy & Invocation Magic & Consummate Talisman) the total combined bonus from all Names cannot exceed your Magic Theory score - so high value names are not that much better than smaller ones.
At the end of the day, a magus who works hard to build up a collection of known Names can get +MT bonus to "some" lab work and/or spell casting.
The cap of +MT is deliberate - no matter how many names you combine, you still have a limit.
This magus must also go around shouting out praise to pagan names in public. Talisman effects have to have the (bold) sound of the Name as a trigger, and spells using Names must sound out the Name... you can't use names quietly or silently.
Most honest Christian folk of Mythic Europe look darkly upon the magician who invokes and praises the false pagan gods, much more than those who just work magic (or those who invoke the Saints.) Even grogs look worried at all this pagan worship... It can restrict your magic in many public places.... Heck, TMRE points out that many magi disapprove, including significant numbers of Quaesitors (who fear the wrath of mundanes upset by all these pagan names).
The big split between Theurgical/Name magic and Spirit Magic is the way Spirit Magic tries to abstract out the power and work with anonymous elementals and such, and to try to placate the Church and claim its magic is not idolatrous. Theurgists and Name magi try avoid drawing too much attention to their ways (and to have non-Name magics to fall back on when in public!)
(And no, Saints names are all Divine not Magical, and don't work with (Magical) Names of Power Virtue).
As for the rest of the question: Pilum of Fire, Ball of Abysmal Flame, Prison of Flames and Burst of Flames all fall under the categories of Flame, Fire, and Ignem.
Sooo, to use this, you would have to:
Cast the Muto/Vim spells/effects (in the case of an item) before hand.
If you were using more than one spell/effect (name) then the first one would have to have a duration that would allow you to cast (ridiculous alert!) say nine more spells, BEFORE you cast the spell you wish to use....
This conflicts with "D: Special" (pg 76 left top)
Come up with a listing of Names and the bonuses for each one... 
plus
Um, you can use Angel names, planets (of course they are greek mostly) Faeries etc....The only restriction I see is the insert at the top of the page......Also, I would like to point out that a name spoken amongst a grouping of Latin words, unless its a REALLY well known entity, would go completely un-noticed by most peasants...(They don't speak Latin, or would be unfamiliar with the name in any case).
I admit, I missed the part about Lab total...Where is that located?
the D: Special means "the base level lets you cast one non-Names-of-Power spell immediately after this, or after a series of Names-of-Power spells".
You can chain them, but can't pause and then cast; and you can cast a long-casting-time spell such as a Ritual.
If, on the other hand, you want to simplify the casting of several normal spells, pre-cast your NoP but with extended duration, then any spell (that benefits from NoP) begun during the extended duration will get the boost.
remember that Names Of Power always work with "some other Virtue"? The bonus from NoP is used according to that other Virtue...
The one I was referring to was Hermetic Theurgy where the 3 classes of Invoke spells can be invented with Names of Power designed in, in which case the invention lab-work gets the NoP boost as well.
(Yet another way that Theurgists are better at summoning Daemons than non-Theurgists...)
Ok thats cool. It would really stink if the spells had to have extended durations. The first one you got you would have to have extended duration in anticipation of getting others...
Now THAT's really cool. If you had Sun duration, you could (stupid alert) cast like all your NoP spells at the begining of the day, and get those bonuses all day...Well at least until you use that type of spell...
Ah. Didn't pay much attention to that section... 
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S&M bonuses are a sensible guideline, but since there are several canon S&M that grant substantive bonuses to Techniques and Forms, I would definitely expect some Names to do the same.
Several pagan god archetypes can justify an Ignem or Fire significant bonus: e.g. Apollo, Helios, or Lugh (or any sun-god) look quite fitting for an Ignem bonus, Efestos, Loki, or Agni (or any fire-god) for a Fire bonus.
Flipping through the pages of any good text about European and Near-Eastern pagan mythology (Norse, Slavic, Celtic, Greek, Egyptian, Babylonian, etc.) should give you plenty of ideas about Names of Power. Cross-reference aspects of pagan gods with S&M guidelines, and you are a theurgist in business.
This is not entirely correct, since there are several S&M bonuses up to +4 (e.g. Hickory for Ignem, Cinnamon for Imaginem, Jade for Aquam, Mercury even + 5 for Muto), so I'd say that +4 is a more sensible cap for Form/Technique bonuses, at least for Forms.
Quite true. I'd just mention that you may also stack bonuses from Names and thematically-similar Mystery Virtues: e.g. in my opinion and experience, a Merinita theurgist can find extremely beneficial to combine bonuses from Names of Power and faerie charms, and the mysteries somehow overlap in theme.
And as with vanilla Hermetic magic, it's also a matter of choice between more powerful, but narrow, specialized names or less powerful but flexible in application, general ones: e.g. does your character opt to develop the +3 Ignem Name or the +6 Flames one, different aspects of the same god-Archetype (for Greek gods, they'd be different epithets of the same god) ??
True, to a degree, but definitely be mindful that this will vary from saga to saga. Talk with your troupe about how much your Hermetic magi are going to be mindful or worried of the Church in your saga, and consider how much your character cares about the Church and its teachings, or fears its disapproval. E.g. an outspoken, proud Pagan or Depraved Flambeau, Tytalus, Merinita or Ex Misc magus is not going to have such coward concerns, bets fit for Jerbiton, Quaesitor, and Trianoma wussies and Christian sell-outs. 
True, but Name Magic is so much more cool 
(except for Spirit Familiar and Inscription Over the Soul: any serious theurgist should work to develop these virtues as well, if their mystery path allows them -any one that has Ascension as a goal will do).
Glad you think Name Magic is cool - it is meant to be! (Fun Things, at a price...) Spirit Magic being abstracted and made "more acceptable" means also that it is less cool and flavoursome.
Spirit Familiar is explicitly available to Theurgists - indeed they have their own superior variant (Theurgic Spirit Familiar) which allows binding the aspect of a (cooperative) Daemon as a Familiar Spirit.
Inscription On the Soul is also good for Theurgists (or any other magi) but doesn't get listed under Theurgy as (despite being cool) it doesn't involve the name aspects of Theurgy - just your own spirit...
One of my favourites is the (non-Theurgist's) trick of binding S&M bonus items into your own body, so the living body is the Talisman - lots of power (and the odd few warping points... hey ho!)
Ok..I get all this...but Agnar's question still remains...
How many names do you know????
Sure I need to make a spell/effect etc, but I still need a name...
How many do I know?
Example....
Real quick now...
Name as many of the declared Saints of the Church...
(yeah, doesn't fit NoP, but the idea is the same...YOU, HAVE to know the names before you can put them to magic. You also need some sort of background for each name...
What do you use?????
There must be a lore here that can be used...
Yes, but Inscription On The Soul is quite well darn useful (as well as Theurgic Spirit Familiar) to accomplish any Ascension in an efficient way. So IMO it just makes sense that these two Virtues had been fully incorporated in the lore of any mystery cult that has Ascension as a goal. It doesn't involve name magic as such, but it is strongly linked to the end point of most name magic traditions. So initiation scripts for them should be known and relatively common. It's just that differently from Spirit familiar, theurgists haven't (so far) developed a specific, distinct variant of their own.
You know as many names as you care to research and develop. They are but special kinds of MuVi spells, after all (thinking of Invocation Magic, which is going to be their most typical and common use). IC, Hermetic mages will typically use names of pagan deities, which means they will use Magic Lore and Faerie Lore, essentially. OOC, the player should gorge on lore about ancient pagan mythologies of Europe (esp. Greco-Roman, Norse, Celtic, and Slavic) and Near East (Egyptian, Sumero-babilonian Pheonician, etc.). Hermetic mages would likely have more accurate lore on pagan european religions, however.
Cross-reference the various portofolios of the gods and goddesses with the S&M guidelines.
Ahhhh, now we get to the meat of it...
So ML and FL...And how many names do you know (Repeating myself)?
One pantheon per point? This though seems too expensive. It not that hard to get a list of names and who they are, so its not inflative as an ability...Perhaps a Lore score say in 'Norse' mythology, Greek mythology etc...A '1' in each might do...
Like I said above...you CAN'T make the spell if you don't know the Name...
That statement is incorrect if you don't look at it the right way.
The spells are the names of power, the names of power are the spells.
As far as knowing the identities of entities about whom to learn the names, the book is not explicit but I get the feeling that the selection is sufficiently large that running out of names is no more than a theoretical concern and that finding an appropriate entity for which to learn a name of is not intended to be a challenging task.
Thanks Erik, but I will reiterate...I don't seem to be getting my point across...
When you cast the spell, you speak the name, which draws the entities attention, and enables the bonus.
Like you said, the Name is the Spell...
So...When you speak Jupiters name, and invoke his power...Where did you get HIS name?
I could use ANY name here, I just use a well known name for ease of use...If I used a less known name, perhaps it would help illustrate what Im getting at better (dang internet).
To Cast the spell, and To make the spell, you need a name. HOW did you get it? You can't just make up an entity to fit your spell desire... You need to KNOW the entity and his name. This means you need to know something about him...ie...fire god, air demon whatever...You need to come by this information somehow...
Therein lies the question...
How to express this knowledge...
Presumably the name itself, even the aspect of the name, is known by the magus somehow (an appropriate realm lore to represent it, or perhaps simply taking the names magic virtue is enough to show that you've studied them), and the research is to figure out how to apply the name to your magic.
Edit: You mentioned in your original post about tying it to an ability, such as realm lore. I don't think it needs to be limited in such a mechanical way. Naming magic might very well contain enough lore to adapt any powerful being's name to something it's sympathetically linked to, and the character probably starts with a hundred or so names known, just from learning the virtue. The player's already limited by the process of inventing the MuVi spells - I don't think it's necessary to put a limit on the number of those as well.
How would you know what (entity) is linked to?
Sure you could say that you start with a list of names from initiation..but how many do you know?
Does this mean that you automatically know EVERY entity that has anything to do with Fire? Water? Does this mean that you know the name of every entity in Europe, Asia, and Africa, that could possible give a bonus?
This is more or less what Im getting at...How much do you know? this becomes important when you start stacking (say) bonuses for a fire spell. You would need a different entity for each spell...Each entity implies a different pantheon/group in MOST cases...kind of like saying fire in ten different languages...you need to know at least a little of each...
Apparently, Magic Theory gives you the knowledge you need to figure out, assuming you know anything about the named entity at all, what the name can be used for.
It does, after all, limit how much you can add as a bonus. Magic Theory's also how you 'know' the various shape and material bonuses, which this is very similar to.
Maybe you don't necessarily start with a list of names from initiation. At the very least, though, you're able to find sympathetic magic in powerful names in general and, if you know anything about the deity or whatever's portfolio, you can figure out some limited aspect of that portfolio for which the MuVi spell will give a bonus.
Probably you would have to study a little about the deity. But if you're taking Names of Power, you're likely in a mystery cult, and they probably have books and books full of them. It probably doesn't take a whole season to learn a name, so simple access to some lore about various names should be enough to develop any MuVi name spell you need.
Edit: From your frustration, I'm guessing you want a harder limitation on it than this. I understand if you disagree with my suggestions; the virtue as written seems to intend that the players can make up Names of Power and research them, just as they can make up spell spirits for theurgy and so on. So my goal's just to justify the mechanics in a flavor sense, while yours seems to be more along the lines of revising the mechanics.
Basically I agree with what Ejidoth said. If you wish a slightly more detailed guideline, assume that any mage with Magic Theory, Magic Lore, and Faerie Lore (heck, no I'm not going to deal with the ultra-thorny issue of which deity belongs to either realm; I simply assume that any theurgist, and for that matter any decent hermetic, should have both, and Infernal Lore as well, if only to be able to recognize different kinds of spirits) will have good knowledge about all the pantheons of major european pagan religions: Greco-Roman, Norse, Celtic, and Slavic. The ones which any mage is bound to find detailed literary lore database about, in Latin: I'm assuming that in the magic-laden ArM universe, classic sources were rather more thorough and abundant in recording lore about non-Latin pagan mythology, which is quite likely. For the same reason, I also assume that lore about the Egyptian pantheon is readily available in the Order; it is at the roots of the whole tradition, after all.
You should also remember that by no means you are limited to 1 God = 1 name. Each god typically is linked to a relatively large set of different attributes, portfolios, epithets, and myths (this is especially true for Greco-Roman and Norse gods), each of which nuances its archetype in different ways and can be assumed as the basis of a Name for the purpose of theurgy. Just to make some typical example, you could probably research various aspects of Apollo to get names for Creo, healing, Ignem, fire, Mentem, Loki for fire, deceit, illusion, Muto, and several others. With a little creativity, I assume that just by using the Greco-Roman, Norse, and Egyptian gods, which any decently-trained Hermetic will know a lot about, you can come up with far more potential Names that you will ever be able to research.