She doesn't use a last name.
女王不用姓氏。

The queen's official title is "Elizabeth the Second, by the Grace of God, of the United Kingdom of Great Britain and Northern Ireland, and of her other Realms and Territories Queen, Head of the Commonwealth, Defender of the Faith." No last name needed.
女王的正式頭銜是“承上帝洪恩，大不列顛及北愛爾蘭聯合王國與其屬土及領地之女王伊麗莎白二世，英聯邦元首，信仰的保衛者。”不需要姓氏。