Yes, because children always took their father's name, even those of a queen regnant. Certainly no monarch would have thought to retain his/her mother's name, which in those days marked you as illegitimate. The choice of Windsor in 1917 was about getting rid of the German association, rather than a decision to alter how dynastic houses were named. The proclamation made this clear:Big RR wrote:Meade--as I recall, Edward (who succeeded Victoria) was of the Saxe-Coburg-Gotha line because f his father, Prince Albert
The intent was that the name would be inherited through the male line only.Now, therefore, We, out of Our Royal Will and Authority, do hereby declare and announce that as from the date of this Our Royal Proclamation Our House and Family shall be styled and known as the House and Family of Windsor, and that all the descendants in the male line of Our said Grandmother Queen Victoria who are subjects of these Realms, other than female descendants who may marry or may have married, shall bear the said Name of Windsor....
So the present Queen, descended in the male line, continued the House of Windsor. George VI had thought to style her children as Royal Highness (previously restricted to male grandchildren of the sovereign), so there was no pressing need for a surname (which would have been Mountbatten). It might have ended there, had not Philip's uncle, already suspected of wishing to use the monarchy to his own advantage, believed (contrary to Victoria's precedent) that it was already the House of Mountbatten. He was overheard by Queen Mary, who was having none of it, and pressed Churchill to do something.
So another proclamation in 1952, the Queen's children would be of the House and Family of Windsor, but once again excluding their descendants in the female line. In 1960, expecting another child, she issued another proclamation, that any of her descendants not styled Royal Highness (but not married women or their descendants), would have Mountbatten-Windsor as a surname.
I expect that, barring some radical dynastic change à la King Ralph, that a future monarch not properly a Windsor by these rules would choose to retain the name.


