The inspiration is most simple: "tremere" is the infinitive form of the Latin verb for "fear" - just as "mercere" is the infinitive form of the Latin verb for "trade".
Both are utterly impossible as Latin names, and no inventor deserves a pat on the back for proposing them.
But the concept of Tremere magi made it into the World of Darkness, and there you are.
House Guorna? While it would fit the House's established history fairly well, it would require a slight change and goes against the House's name in all previous editions. It also doesn't quite sound good, and detracts from the "hero worship" of Tremere the Founder in the House.
Since this is a trademark, a similar but clearly-different name would also not tread on the IP rights I think (just like various "Coke" drinks). So perhaps a more reasonable derivation of the name's meaning?
Pavor or Pavius, meaning "dread", was a real, albeit rare, name.
Trepidus or Tremis is a prejorative nickname, "the trembling".
Attius meaning "fearful" but of Etruscian bent.
Horatius, "to tremble in fear".
Tremonius, feels more like a Latin name.
The best solution would be to license the use of the trademark.
The easy, correct substitution is Tremendus, "fearsome".
It is good Latin, well known in the middle ages - see the Dies Irae - and fits the flawed self-perception of the youngest and most mousy founder.
I am willing to be the test subject. If I could have the permission of Atlas, I would gladly write a three-page-dungeon that some how features the words "Order of Hermes" and "Tremere" in some prominent obvious fashion. I will self publish it on DTRPG. I will sit and wait for a cease * desist letter, I will challenge it, and let them try to sue me. I have no assets and nothing but debt and bad credit. I would love it!
Alas, in this case the legal status of the trademark is clear, at least for Tremere — it is registered. The question is whether Atlas can license it to the whole world to use freely, and that's something that only Atlas can test.
One would need to see the exact terms of the contract under which Atlas can currently use the Tremere name. I suspect it's something along the lines (put in plain terms) "you can do whatever you want with it as long as it's within the Ars Magica universe, Mythic Europe". That would be the most sensible thing, in that the trademark owner has no interest in restricting the use of the name within the Mythic Europe setting, but has every interest in completely blocking its use outside, in particular in the World of Darkness.
So yes, I suspect that any "open" license Atlas could give, whether under the current conditions or under any condition Paragon might be willing to negotiate (unless they are super-nice) would be along the lines "anyone can produce any material they want, as long as either it has no reference to the Tremere or it's set in Mythic Europe". This would mean that any material porting Ars Magica, to, say, a contemporary setting would probably best leave out the Tremere. Which is not a big deal, I think, certainly nothing worth changing the name for.
Note that the House is TreMEre (stress on the second syllable) the verb is TREmere (stress on the first, since it's a third conjugation verb - tremo, not tremeo). As @Oneshot would say, verrrrry different 
That's certainly true, Then again, when Ars Magica first came out, there was worse in terms of grammatical purity. And even in 5th edition, many a magus has a really silly Latin name.
Furthermore, note that one of the pronounciations for Tremere in ArM5 is TreMARE, which is not that different from TREmohr (that's how you pronounce "tremor" in Latin, i.e. shiver, fear, etc.) and it's a reasonable name for the young Tremere to have presented himself with, in that it does not automatically suggest he's the one in fear rather than the one to be feared - though I can see Tytalus making a lot of fun over it! Over a couple of centuries, it could have easily drifted into the spelling Tremere; the real world has seen much more significant drift in names over the same timespan, after all.
The same might hold for Mercere (MerCARE). Maybe he started as, say, Mercator (MerCAHtor i.e. "Merchant" in Latin, but also the same name as the famous Flemish cartographer), and the House name drifted slightly over the centuries.
Note that Baldren asked for the original inspiration/meaning, not for any pronounciation developed over time in the game. 
EDIT: If somebody insists on a detailed history of the name of the founder, how's this:
Guorna and Tytalus might have called him Tremulus ("the trembling guy"). Clever Tremulus then explained this first as Horror Tremulus (a weird but existing classical Latin phrase for "scare causing trembling") and later consolidated it to Tremendus. 
Spoken like a true Tytalus magus! 
I've been off on Fiveer getting people do do me maps for the Venice thing, and it occurs to me that it would be handy for Atlas to give out some sort of logo that can be stamped on the cover of compatible books. Much as there was an OGL mark for D&D. More broadly if Atlas had a set of digital assets for publishers, that might get more people in the metagame. For example I presume a lot of the internal art from the books is work for hire to Atlas, and that Atlas has no particular way of converting those bits of art into revenue, so it would be useful if people could reuse it for fanzines and so on.
To those with knowledge to speak of on this project: Aside from hunting for errata, is there anything else we as fans can do to help aid in the success of the project?
Specifically, I was thinking about bringing up certain ambiguities in the rules like whether accelerated abilities come with Specialties or whether True Faith functions like The Gift for the purposes of undergoing Initiations and so forth...
Too late for errata or other clarifications. That would have needed to be brought up several months ago to be included in the Definitive edition.
What we fans can do right now to help is to back the crowdfunder when it goes live, and tell our friends about it so they too can back the crowdfunder.
That's an extremely good idea. The digital assets thing might also help people's creations to be more unified in looks. And the logo to add would definitely help in both identifying material made for ArMa, and also possibly even publicize Ars Magica if there starts to pop up material that becomes popular.
Some of the companies with community content programmes on DriveThru do this, with art packs licensed for use only within the programme. For example:
https://www.drivethrurpg.com/en/product/181547/tas-ships-and-vehicles-clip-art
A similar bespoke licence ("can be used with any Ars Magica product") is entirely compatible with text released under CC-BY-SA.
Digital assets would be nice. I do not believe a decision has been made on this question yet.
While people are thinking of what they can do to support the game in a year which should bring new interest to 5th edition, some obvious things are:
Do an actual play stream or podcast - apparently these are very popular for attracting people to try different games, and showing how the rules work.
Launch a new play-by-post game - we have a forum here, and I've seen others run games on rpol.net - I haven't seen any new Ars games launched lately, but ones suitable for new players should get tons of interest.
Write up your scenarios - the more scenarios available for people to look at, the easier we make it for new storyguides (and also provide inspiration for SGs whose sagas need something to run this week, or for other people to try their hand at being a beta-storyguide)
There has been a spree of new games over the last few weeks on the discord server FWIW.
I have considered doing this for some of the one-shots I've run. My concern is that I am a lazy SG who likes to steal statblocks from the books, so either my scenario would have a lot of "(see supplement X, p. Y), which is not friendly to new SGs, or I would be violating copyright.
There are two obvious approaches - one is to file the numbers off and describe the NPC or creature in enough details someone can write the stats later (but this does make it less friendly for new SGs - your scenario will still be handy to old SGs who probably have their own favourite statblock to recycle or supplement to borrow from); the other is to ask people if they could create the stats for a.... and then see if anyone volunteers. Some of the post a day crowd seem to be very disciplined at churning out stats.
But who does this? I did last time I ran and now I am reusing my old write-ups, but I don't really see much else.