BuddyPress.org

Here is the solution for anyone who is going to see this post in the future.

1. Install the username change plugin:
https://buddydev.com/plugins/bp-username-changer/
2. Add to the plugins code (bp-change-username.php) on line 163;

xprofile_set_field_data(1, $user_id,  $new_user_name);

3. In your theme function.php file add the follow code to hide XProfile editing:

function bpfr_hide_profile_field_group( $retval ) {
        if ( bp_is_active( 'xprofile' ) ) :     

        // hide profile group/field to all except admin 
        if ( !is_super_admin() ) {
                //exlude fields, separated by comma
                $retval['exclude_fields'] = '1';  
                //exlude groups, separated by comma
                //$retval['exclude_groups'] = '1';
        } 
        return $retval;         

        endif;
}
add_filter( 'bp_after_has_profile_parse_args', 'bpfr_hide_profile_field_group' );

I hope this helps anyone who finds it.