Windsor is not strictly a surname of the Royal Family either; it is an official designation, as in Royal House of Windsor.
In 1917 the Royal House and Family was renamed Windsor from the House of Saxe-Coburg-Gotha, by an Order-in-Council of King George V.
The Order referred to male-line descendants of Queen Victoria but not necessarily to female descendants. In 1952 Queen Elizabeth II ended confusion over the dynastic name when she declared to the Privy Council her �Will and Pleasure 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.�
In 1960 The Queen issued another Order-in-Council, confirming that she and her four children will be known as the House and Family of Windsor, and that her other male-line descendants (except those who are "HRH" and a Prince or Princess) will take the name "Mountbatten-Windsor".