Are magi names unique?

There is technically only a small number a Hermetic Magi, that have existed for, perhaps, 10 generations at most (generation being time for apprentice to gauntlet to teaching his own apprentice)

How likely is it that two different Magi would have the same name?
I am asking becuse I was checking through the HoH:S book, and under the Flambeau chapter is a mention of "the school of Ebroin", while in the Ex Miscellanea chapter the Primus is named Ebroin.
I suspect it is unlikely that they are the same magus, as Primus Ebroin is said to be young, immature and an orbis, while it seems unlikely that Flambeau Ebroin could have had enough time to accrue enough fame to get a school recognised and named after him, made orbis in a way he doesn't lose the fame/school name, and still be considered young.

Not even close to unique - in the Jerbiton chapter of the same book, it's mentioned that there are so many young magi named some version of Constanta/Constantine that they've started taking on second names to distinguish themselves (HoH:S page 43).

It is mentioned in Against the Dark that the Tremere enforce a "one name, one maga" policy in the Translyvanian tribunal, and resolve competition for who gets the name with Certeman.

I also believe there are several Justinas in House Guernicus.

That is what I get for skimming through the book. I had read the inset above.