I don't think there's a definitive answer. After all, some people have names that can't even be expressed in UTF-16...

There are some odd people out there, who will give their kids the craziest of names, including putting in weird punctuation, accents that don't exist in their own language, etc.
However, you can place arbitrary restrictions on your database. If you want to you can insist on 7 bit ASCII names. It's slightly rude to users, but they'll live with it. It certainly makes searching easier.
My colleague's daughter is named Amélie. But even some (not all!) official British government web sites ("Please enter the name exactly as shown on the birth certificate") won't accept the unicode, so he has to use 'Amelie' instead.