Inasmuch as she has a surname, it's Windsor. The current British royal house is the house of Windsor; that line succeeded the house of Hanover when Queen Victoria died and her son Edward VII succeeded her. Edward took his father's surname, being a member of the royal house of Saxe-Coburg and Gotha; the name of the house was changed to Windsor in 1917, under George V, as a result of anti-German sentiment in WWI. However, in normal usage, the royal family doesn't use surnames -- there's no ambiguity over which Elizabeth is queen of Britain, versus who's Elizabeth Smith or Elizabeth Stone.