Insofar as royals have surnames, his would be Windsor, not Mountbatten-Windsor.
House of Windsor (Feb 8, 1960)
At the Court at Buckingham Palace, The 8th day of February 1960.
Present, the Queen's Most Excellent Majesty in Council.
Her Majesty was this day pleased to make the following declaration:
"My Lords
Whereas on the 9th day of April 1952, I did declare in Council My Will and Pleasure that I and My children shall be styled and known as the House and Family of Windsor, and that My descendants, other than female descendants who marry and their descendants, shall bear the name of Windsor:
And whereas I have given further consideration to the position of those of My descendants who will enjoy neither the style, title or attribute of Royal Highness, nor the titluar dignity of Prince and for whom therefore a surname will be necessary:
And whereas I have concluded that the Declaration made by Me on the 9th day of April 1952, should be varied in its application to such persons:
Now therefore I declare My Will and Pleasure that, while I and My Children shall continue to be styled and known as the House and Family of Windsor, My descendants other than descendants enjoying the style, title or attribute of Royal Highness and the titular dignity of Prince or Princess and female descendants who marry and their descendants shall bear the name of Mountbatten-Windsor."
(London Gazette, issue 41948, Feb. 8, 1960, p. 1/1003. See also the Times Feb 9, 1960 p. 10E.)
