WordPress Query posts that have title > another title

You can use get_page_by_title to match the title of the required post.

$post_name = get_page_by_title( 'Post Title' );

$vars = array(
   'name' => $post_name,
   'paged' => $page, 
   'posts_per_page' => intval($posts), 
   'order' => 'asc', 
   'offset' => ($offset ? $offset : ''), 
   'orderby' => 'title' 
 );