Using hook_menu in a custom module, how do you add a menu item to more than one menu in Drupal 7?
I'm pretty sure you are looking for menu_link_save() as adding the menu_name in hook_menu() just puts this callback in that menu instead of defaulting it into the navigation menu.  So, after creating it above, with or without the menu_name, you should be able to add it to any other menu(s) with menu_link_save().