When you think of Merlin, he is the most recognisable wizard of the British Isles.
The matter of France speaks volumes on Maugris, and even Atlantes.
Ancient Georgia is the homeland of Medea.
Are there named/famous Wizards for other regions of Mythic Europe?
Outside of ME, Japan has Abe no Seimi. Korea has Jeon Woo-chi
Virgil probably counts as Rome's premier wizard.
I think Pan Twardowski is too long after period to count as ME Poland's national wizard.
Wayland? Circe?
Wayland the Smith is considered the premier wizard of where? Northern England ?
And what nationality/ethnic group claims Circe?
If we look to the Kalevala, we might get an idea of the archetypal Finnish wizard
I forgot about Erichtho, in Thessaly
Odin in scandinavia. (Denmark, Norway and Sweden, plus Iceland and the Faeroes i suppose).
He's from germanic tradition, so I'd assume Northeren Germania/Scandinavia. If I understand correctly, the stories of Wayland Smith was brought to Scotland/Northern England by the vikings involved in the Kingdom of the Isles. I may well be wrong.
I'd assume greek/macedonian. Possibly Thessaly, which was considered steeped in magic at the time from what I understand.
I must also admit I was associating Medea with the Hydra, which I've mentally associated with the Krim (Cremea) peninsula.
Works for me.
Medea was from the ancient kingdom of Colchis, located on coast of the Black Sea, where Georgia lies today.
Her aunt Circe lived on the fictional island of Aeaea. Where that was located is unclear - Homer didn't say, but at least some later authors put it near Italy.
Thanks! Time for me to memorize that - I haven't read those stories in decades.
England, with Wieland for continental Germanic people. It's the same character, but each woth a little national sauce (a la American gods)
Interestingly, his Estonian variant, Kalevipoeg isn't much of a wizard, merely a giant.
She'd be Greek cultured (like of Southern Italy was), and IIRC her island of Aeaea was supposedly not far from Sicily just a few days' sailing from Charybde and Scylla on the western side of it, since she needs to cross it to go back to Colchis.
Other key magicians:
France : Melusine, though more in the faerie direction.
Germany: Doctor Faust (though later than the 1220 start)
i had thought that there was a wizard named Math in Finnish folklore, so I googled him. Turns out he's Welsh.
Yes, Math ap Mathonwy would be a good choice for Wales, not Finland, along with Gwydion and Arianrhod. The Mabinogion is a rich source of tales, but other than Lloyd Alexander's YA novels, it is rarely referenced in fantasy.
While more Mythic Middle-East than Mythic Europe, we should not forget King Solomon.
Sounds like a trollsynir to me 
(Hey! Quotes working again for me! ^^)
How about Al-Khidr for the Middle East, although I can't narrow it down geographically more than that.
According to Wikipedia, he hung out with Moses, the biblical figure, so that puts him around Egypt, at least at the time.
What about Morgana - Sorceres or Fae? at least good in Illusion and known everywhere - even in Arabia, after her they named the Fata Morgana.
Does her fame as a wizard/magician/sorceress outweigh Merlin?
Basically, I am looking for the most prominent name of a magic user that a character from a particular region would name if asked "Who is the greatest magician?"
I would have thought that a character from Britain would answer "Merlin".
Though a Welsh character might say "Gwydion" or "Math" instead.
French characters mught name "Maugris" or "Atlantes"
etc.
For lots of regions there aren't really any famous magicians. In their older tales nearly all the magical stuff is done by gods and similar, and in newer tales the miracle-workers are saints and holy men.
Fully accept that not all regions have their own named wizard.
However, trying to compile a list of those that do.