The "Royal Family Name" article on the official website states:
"Unless The Prince of Wales [Charles] chooses to alter the present decisions when he becomes king, he will continue to be of the House of Windsor and his grandchildren will use the surname Mountbatten-Windsor."https://www.royal.uk/royal-family-name
The "unless" is a bit odd - by the time of the article's publication, shouldn't then-Prince Charles have known whether or not he intended to alter the name(s) when he became king?
Originally Posted by Duke of Leaside
The problem was Mountbatten was wrong; he was a generation early. Under normal circumstances it would still be House of Windsor under Queen Elizabeth II and only switch when Charles became King (i.e. now).
Queen Victoria was the House of Hanover - it didn't switch to Saxe-Coburg-Gotha until her son Edward VII acceded.
But if the Victoria and Edward VII precedent was considered correct, then the children also ought to have been surnamed Windsor from birth along with the title of Prince and Princess of Greece...