According to the
monarchy's website it is not required for the baby to have a surname, because prior to 1917 members of the royal family did not have surnames as they adopted the name of the house or dynasty to which they belonged. If the duke and duchess decide to include a surname, there are three choices available: Mountbatten-Windsor, Wales, or Cambridge. In 1917, King George V replaced his house name with Windsor, from Windsor Castle, while Prince Philip adopted the surname Mountbatten from his British maternal grandparents. The couple could also decide to keep it simple and leave it at "His/Her Royal Highness Prince/Princess of Cambridge."