Excluding a page with a certain name from wp_page_menu

How about using get_page_by_path(), then using the ID from the returned object in an exclude filter?

add_filter('wp_page_menu_args','my_nav_exclude_pages');

function my_nav_exclude_pages( $args = array() ) {
  $homepage = get_page_by_path('my-page-slug');
  $args['exclude'] = join( ',', array( $args['exclude'], $homepage->ID ) ); 

  return $args;
}