Need post_type_archive_title function but in ‘single’

There doesn’t appear to be one, but the following should work:

//Get post type    
$post_type_obj = get_post_type_object( get_post_type() );
//Get post type's label
$title = apply_filters('post_type_archive_title', $post_type_obj->labels->name );        
$archive_title = apply_filters('post_type_archive_title', $post_type_obj->labels->all_items);

This can, for instance, be put in one generic header template that is applied to all single-cpt files. With is_single() it can be put in an even more generic header template.

For a complete list of labels, see http://codex.wordpress.org/Function_Reference/register_post_type#Arguments