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The British Royal Family changed their last name from Saxe-Coburg-Gotha to Windsor in 1917. So Her Majesty's last name is Windsor. Windsor. Some of her family are entitled to use the name Mountbatten Windsor which was authorised by an order in council in 1960.
Therefore, Mountbatten-Windsor is the surname of all male (and unmarried female) descendants of Prince Philip and Queen Elizabeth II; this includes Prince Charles, Prince William and Prince Harry. Because Prince Harry and Price William use the title Prince, they do not use the last name Mountbatten-Windsor. They use the surname Wales because they are the sons of the Prince of Wales. Although Royals don't tend to use a last name, in the instance of a marriage, for example, Prince William's last name is Mountbatten-Windsor. This is the surname of all descendants of Prince Philip and Queen Elizabeth II (excluding females who marry).