What is Queen Elizabeth II surname?

Answer 1

Technically, she does not have one, but is from the House of Windsor.

Elizabeth never uses a surname. Her dynasty is called the House of Windsor, but I think it would be perceived as a terrible insult to address her as Elizabeth Windsor.

Some background material from the Wikipedia article on Windsor:

By virtue of Queen Victoria's marriage to Prince Albert, son of Duke Ernst I of the small German duchy of Saxe-Coburg and Gotha, Victoria's descendants were members of the ducal family of Saxe-Coburg and Gotha with the house name of Wettin. Victoria's son Edward VII and his son George V reigned as members of this house. However, high anti-German feeling among the people during World War I prompted the Royal Family to abandon all titles held under the German crown and to change German-sounding titles and house names for English-sounding versions. On 17 July, 1917, a royal proclamation by George V provided that all agnatic descendants of Queen Victoria would be members of the House of Windsor with the personal surname of Windsor. The name Windsor has a long association with English royalty through the town of Windsor and Windsor Castle.

Her family name is Windsor which was changed to Windsor when she was a child. She is married to Phillip Mountbatten, a prince of Greece and Denmark.

Answer 2

She has no surname; she doesn't need one because she's the Queen.