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'
);