Hi Alex,
As far as I know, WordPress does not allow Umlauts in usernames, while BuddyPress does allow them in profile fields, including Name, Nickname, and Last Name.
When you search for ä, ö, or ü, BP Profile Search also searches for a, o, or u, (and vice versa) e.g. if you search for pöp or pop, you will find both pöp and pop.