Language / label changes?

This is actually controlled by the WordPress core, inside the get_the_title() function.

Try this hook in your theme functions file:

/**
 * Tribe Events: Replace 'Private: ' title prefix from events
 */
function tribe_events_remove_post_status($title, $id) {

  $cpt = get_post_type();
  if($cpt == 'tribe_events') {
    $title = str_ireplace('Private:', 'Internal Only:', $title);
  }
  return $title;
}
add_filter('the_title', 'tribe_events_remove_post_status', 10, 2);