Ok,
now I found something.
In UTF-8 a small ö and a strtolower(ö) is not the same, that is the Problem.
In the login.inc.php on row 74 there is a MySQL SELECT statement,
...WHERE lower(user_name) = '".mysql_real_escape_string(strtolower($request_username))..., that is the cause of the Problem.

But I don't understand why in this Forum it is no Problem to Register Usernames with äöüß.

I am hopeful we can find out a solution.

Gregor