Under an Order-in-Council in 1960, the non-titled descendants of Queen Elizabeth and the Duke of Edinburgh were given the surname
Mountbatten-Windsor, combining the surnames of Elizabeth and Philip. However though titled, the Queen's children have all decided to use the surname also in honour of their father.
As with Royal Family tradition, Prince William uses "Wales" as a last name, as has Prince Harry. William's York cousins in turn use "York" (other Royal Families also use their parents' title as their own working surname). Past precedent however is that such title-surnames are dropped from usage in adulthood, with either title alone or name and
Mountbatten-Windsor being used on legal documents and banns of marriage.
http://en.wikipedia.org/wiki/Windsor-Mountbatten