Have there been any other Lords or Ladies who were the great-grandchild of a monarch and then promoted to prince or princess once their grandparent ascended the throne?
I don’t think so because the last time the UK had a monarch with great-grandchildren, there were different Letters Patent in operation. Under the previous LPs, great-grandchildren in the male line would have a princely title, but would be His/her Highness rather than Royal Highness. In fact, the Queen’s father, George VI, was born a mere Highness, rather than a royal one, although he got promoted by Queen Victoria before she died.
To address another question upthread, whether or not Sussex will ever be used as a sort of surname for Harry and Meghan’s children probably depends on whether those children assume royal titles. If they don’t, they would be similar to James Severn and Louise Mountbatten-Windsor, who follow the conventions of holders of aristocratic titles. They don’t use Wessex as a surname. It’s not common for the son or daughter of a duke to call themselves Lady Jane Spencer-Churchill of Marlborough, for example.
If the children assume princely titles when the Queen dies, which under the present LPs could happen, then they would be, for example, Prince Philip of Sussex or Princess Alice of Sussex and probably be known informally as Philip Sussex and Alice Sussex.
As for the Mountbatten-Windsor surname, it’s actually a bit complicated, but essentially, as I understand it, children in the male line from the Queen and Prince Philip, who are not Royal Highnesses, have the surname Mountbatten-Windsor. The Royal House of the UK remains Windsor.
As it stands at present, let’s say that Meghan has triplets, two boys and a girl, first names chosen by me. They would be Philip Mountbatten-Windsor, Earl of Dumbarton, known familiarly as Philip Dumbarton or more formally as Lord Dumbarton. The second son would be Lord James Mountbatten-Windsor, addressed formally as Lord James. The girl would be Lady Alice Mountbatten-Windsor, addressed as Lady Alice.
(I had to edit the first sentence of this because I wrote “we had a monarch”. Then I had to remind my American self that no, Victoria was not my monarch.
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