Lilibet Diana Mountbatten-Windsor was born last Friday at a hospital in Santa Barbara, California.
But the Sussexes’ decision to use the Queen’s highly-personal pet name for their second child has already sparked a row.
Lawyers instructed by Harry and Meghan said it was “false and defamatory” for the BBC to suggest the couple did not ask Her Majesty if they could use the name.
The Duke and Duchess claimed they would not have used the name if the Queen had not been “supportive” of their choice.
But rather than confirming the Duke and Duchess’s version of events, the Palace refused to deny suggestions that the Queen was “never asked”.
The Daily Telegraph understands the Queen was “told” about the name after the baby was born last Friday, rather than her permission being sought in advance.
It suggests that if the Duke and Duchess chose the name to curry favour with the Queen and the wider Royal family, the tactic has backfired badly.
A spokeswoman for the Sussexes declined to comment.