conditional: if is page, and all subpages

Use get_ancestors to get the page parent, then check against that value instead of checking against the name.

$ancestors = array();
$ancestors = get_ancestors($post->ID,'page');
$parent = (!empty($ancestors)) ? array_pop($ancestors) : $post->ID;
if (!empty($parent)) {
  switch ($parent){
    case 1 :
      // menu for parent page ID 1
    break;
    case 2 :
      // menu for parent page ID 2
    break;
  } 
}

And so on. Your numbers will need to match against the IDs of the parent pages.