BuddyPress.org

Exactly what error message are they getting?

Are the errors coming from the WP fields – Username
Or the BP field – Name

What names are they trying to use?

BP gives specific errors re usernames, such as ‘Username must be at least 4 characters’.

WP has its own restrictions, I think allowed chars are [a-z] and [1-0].

You should also provide the version of WP and BP used on your site.