using theme_menu_link()
You can get the ID of a menu by looking at the URL when you edit it in the menu configuration admin interface and converting dashes to underscores.

For example, on admin/structure/menu if I hover 'User Menu' I see admin/structure/menu/manage/user-menu/edit which means that the menu machine name is 'user_menu'.

The $element contains the menu's id: $element['#original_link']['menu_name']. 

So you can put that in your if() and get

if($element['#original_link']['menu_name'] == 'user_menu') {
  ...
}


where you replace 'user_menu' with the name of the menu you want.