But the 34-year-old's big reveal might have been spoiled by Prince George, who let the name slip months ago.
Following Wednesday's photo call, the couple introduced their son to the Queen and her husband, Prince Philip, the Duke of Edinburgh.
She said the baby had "the sweetest temperament" and has "just been a dream".
Could the young prince have overheard his Uncle Harry and Auntie Meghan discussing baby names? According to Babble, the name Archie is a variant of Archibald-a name of English origin that means "genuine and bold". In fact, the speculated top pick among British oddsmakers was Arthur, followed closely by James, Philip and Albert.
The baby boy, who is seventh in line to the throne, will be called Archie Harrison Mountbatten-Windsor. Their Royal Highnesses' son weighs 7lbs. 3oz.
Hours after Kensington Palace confirmed Markle had given birth on Monday, Prince Harry spoke to the media and said mother and baby were doing "incredibly well".
Meghan had her mother Doria Ragland by her side as she gave birth and Doria was "overjoyed by the arrival of her first grandchild". "But his looks are changing every single day, so who knows".
Instead, the Duke and Duchess of Sussex have chosen Mountbatten-Windsor, in keeping with family tradition-and including a nod to the Duke of Edinburgh. "We are just so thrilled to have our own bundle of joy and to be able to spend some precious time as he slowly starts to grow up". The infant is the eighth great-grandchild of 93-year-old Elizabeth, Britain's longest reigning monarch.
Harry is due to return to royal duties Thursday, attending an event in The Hague for the Invictus Games sports competition for injured service personnel and veterans.
Prince Harry was talking about the coming weeks.
George was visiting grandmother Carole Middleton with sister Charlotte when they came upon a woman walking her dog, The Sun reported at the time.