drupal 9

    $menu_name = 'my_custom_menu_machine_name';
  
    $menu_tree = \Drupal::menuTree();
    // Build the typical default set of menu tree parameters.
    $parameters = $menu_tree->getCurrentRouteMenuTreeParameters($menu_name);
    // Load the tree based on this set of parameters.
    $tree = $menu_tree->load($menu_name, $parameters);
    // Transform the tree using the manipulators you want.
    $manipulators = [
      // Only show links that are accessible for the current user.
      ['callable' => 'menu.default_tree_manipulators:checkAccess'],
      // Use the default sorting of menu links.
      ['callable' => 'menu.default_tree_manipulators:generateIndexAndSort'],
    ];
    
    $tree = $menu_tree->transform($tree, $manipulators);

    $menu = $menu_tree->build($tree);

     // Set theme for custom styling.
    $menu['#theme'] = 'my_custom_theme';