Get rid of the word private in bbpress forums names

AFAIR BBPress relies on WP functions with these titles, so most probably this will be helpful:

function remove_private_prefix_from_title( $title ) {
    return '%s';
}
add_filter( 'private_title_format', 'remove_private_prefix_from_title' );

And here you can find docs for that filter: private_title_format