There’s good article by the W3C called Personal names around the world that explains the problems (and possible solutions) pretty well (it was originally a two-part blog post by Richard Ishida: part 1 and part 2)
Personally I’d say: support every printable Unicode-Character and to be safe provide just a single field “name” that contains the full, formatted name. This way you can store pretty much every form of name. You might need a more structured storage, but then don’t expect to be able to store every single combination in a structured form, as there are simply too many different ones.