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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.
Prince William isn't typically called by his surname and although Kate Middleton has a known last name, she is called Catherine, Duchess of Cambridge. Prince Harry and Prince William get their last name from their father, Charles, Prince of Wales. last name is not required for the royal baby, as he will be given the title HRH Prince, but Kate and Prince William can choose a last name for their baby.