Had Queen Elizabeth been born just about a decade earlier, her last name might very well have been different. However, due to tensions related to World War I, the family changed their last name in 1917.
Queen Elizabeth was born on April 21, 1926. Her full name at birth was Elizabeth Alexandra Mary, and she was born of the royal House of Windsor. Therefore, Queen Elizabeth's last name is Windsor.
She married on November 20, 1947 to a man whose name was Lieutenant Philip Mountbatten. He had been born Prince Philip of Greece and Denmark; however, he renounced the titles and became a British subject when he married Queen Elizabeth. Elizabeth, did not adopt the tradition of taking her husband's last name. In fact, on April 9, 1952, she announced "that I and my children shall be styled and known as the house and family of Windsor, and that my descendants who marry and their descendants, shall bear the name of Windsor." She changed that direction in 1960 by declaring that the surname of male descendents was to be Mountbatten-Windsor when they are not using their title (i.e. Wales, York or Wessex)
Queen Elizabeth's paternal grandfather's ancestry has been traced back to Germany. The ancestors such as Frederick and Dedo I belonged to the House of Wettin in the 900s. After they inherited the Wettin Castle, they took on the last name of Wettin. Wettin Castle was located near Wettin in Saxony, Germany. Wettin would have been Queen Elizabeth's last name if her family would have kept on with that name.
Until 1917, the name of the family that Queen Elizabeth was born into was the House of Saxe-Coburg and Gotha. Her father, King George VI, was born in 1895 with that last name.
However, on July 17, 1917, Queen Elizabeth's grandfather, King George V, announced that he and his family would become the House of Windsor. The reason for this movement was because England had major feelings of discontent against Germany due to World War I.