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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.
Her surname is Windsor. Royals had no surname up until 1917, but if they needed one, would use the name of their House, or dynasty. Thus, immediately prior to 1917, they used Saxe-Coburg-Gotha, being the ruling House at that time.