They have not chosen a grander title for the baby, who is not a prince but could have been named a lord.
Baby Archie will be the first descendant of Prince Philip and the Queen to bear their joint name full-time.
He was also given a baby toy, a soft cube with a bell and a mirror, by 7-year-old Daimy Gommers, whose father Paul has competed for the Netherlands in the event.
"In 1960, The Queen and The Duke of Edinburgh decided that they would like their own direct descendants to be distinguished from the rest of the Royal Family", according to the Royal Family website.
"[The Duke and Duchess of Sussex] are so incredibly grateful for the warm wishes and support they've received from everyone around the world, since welcoming their son two days ago", another caption read.
While not now a prince, when Prince Charles becomes King, Prince Harry's son will automatically become His Royal Highness Prince Archie Harrison Mountbatten-Windsor.
Left: Princess Diana holds Prince Harry after his birth in 1984, while standing next to Prince Charles.
Instead of inheriting an earldom as expected, the couple have decided their son will be known asArchie Mountbatten-Windsor - a surname directly inherited from his great-grandfather.
As the world reacted to the exciting royal baby news, Queen Elizabeth herself was said to have been "delighted" by the arrival of her eighth great-grandchild. They elected to spend the first two days as new parents away from the media spotlight before presenting him to the public at Windsor Castle on Wednesday 8 May.
Speaking to the press, Meghan said: "It's magic". He has the sweetest temperament, he's really calm'.
"Above all he said he was just amazed by the miracles in the world, and how his child has made a lot of people happy", van der Stroon added. "He's already got a little bit of facial hair as well, wonderful".
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