Output the menu name in WordPress

wordpress_menu_name.php

<?php
/* This function returns the menu name */
function wp_nav_menu_title( $theme_location ) {
	$title = '';
	if ( $theme_location && ( $locations = get_nav_menu_locations() ) && isset( $locations[ $theme_location ] ) ) {
		$menu = wp_get_nav_menu_object( $locations[ $theme_location ] );

		if( $menu && $menu->name ) {
			$title = $menu->name;
		}
	}
	return apply_filters( 'wp_nav_menu_title', $title, $theme_location );
}
/* Then in your theme you'll want to echo it out. e.g. <h3><?php echo wp_nav_menu_title('document'); ?></h3>
*  The menu location is set in your register_nav_menu in functions.php
*/
?>