In the case of European nations it would be specific to each nations use of the roman alphabet or others. If the way teh roman althabet is used for the official language there is radically different then names from nearby nations I would imagine that immigrants would change their names to the spellings of their new nation once nationalized (gaining citizenship there) but maybe they would retain their previous nation/peoples last names and first names or religon. It really depends on teh nations.
In fact, that's exactly what happened in the past. Just a few examples:
Nowicky->Nowitzki (Polish->German)
Markwart->Marquard (German->French)
etc.
I agree with your sentiment on the hair colors of Asian people, and Japanese in particular. I had a blonde Japanese SF until recently. While that sure was fun, I don't think there are that many blonde Japanese guys around (I don't know a single Japanese who is blonde, and I do know quite a bunch). Giving them a 1% chance of being blonde or ginger seems ok to me, but any more than that sure seems very very unlikely.