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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.
Willam and Harry do have a last name; they are known as William Windsor and Henry Windsor. You might hear that they are also called William of Wales and Henry of Wales; that is another title, but their last names are now Windsor. Their last name is Windsor. William is the Prince of Wales.