BuddyPress.org

There’s a few ways to do this, and it depends on where you are in the site and what information you might already have available, and if you want the current user, or a user in a loop of some kind.

If by username you mean their user_login name, sometimes you can just do…

bp_core_get_username($user_id);

…where $user_id is the ID of the user you’re looking for.

Let me know if this doesn’t work in your situation?