The couple named their baby boy Archie Harrison Mountbatten-Windsor after he was born on May 6 2019.
Meghan is said to have told the parent of a little boy called Harrison that she and Harry could not decide whether to choose Archie or Harrison as a first name.
Sherry McBain, 42, who lives in Southampton, said her wife Mandy brought their little boy Harrison to a children’s book reading attended by Meghan at the games in The Hague, and the pair got chatting.
Ms McBain told the PA news agency: “She was like ‘Harrison, that’s Archie’s middle name’, and Mandy was like ‘Yeah, I know’.
“They were just having a chat because Harry and Meghan couldn’t decide between Archie and Harrison for the first name.”
Archie means “genuine”, “bold” and “brave”, and is German in origin.
Short for Archibald, it is now given as a name in its own right.
Harrison means “son of Harry”, so its inclusion in Archie’s full name is likely to have been a tribute to the duke.
Archie entered the top 10 names for boys in England and Wales for the first time in 2020, according to the latest data from the Office for National Statistics (ONS).
Archie saw a surge in popularity, jumping 10 places from 19th to ninth.
There were 2,944 babies named Archie in 2020, up from 2,544 in 2019.
Harry and Meghan named their daughter – born on June 4 2021 – Lilibet “Lili” Diana.
Lilibet is the Queen’s family nickname and the couple refer to their daughter as Lili.
Ms McBain, a nursing officer in the RAF, said of the book reading at the games: “My little boy Harrison was just over the moon that a princess has read him a story, so that went down really well with all the UK children.”
She said she was told Meghan was “really open” and “very friendly” at the event.
“Harrison was drawing pictures and telling her that it was a picture of a tram.
“I don’t think it quite looked like a tram, so she was very gracious and said that’s a brilliant tram, so he was delighted,” she said.
Ms McBain, who has been taking part in sitting volleyball and archery for Team UK, said of the Invictus Games: “It’s made a massive difference for me. It’s the difference in the fact that I’m still serving.
“I was diagnosed with delayed complex PTSD. This journey has just meant that actually I can still live a life instead of hiding, and not stepping out of the house and just being broken.
“I owe so much to the Invictus Games and everything that it has done for me and for my family.”
Meanwhile, Daniel O’Connor, 31, from Hereford, picked up a bronze medal in an archery event at the games on Monday.
He spoke about the positive impact Harry has had with the games and how much it means to the competitors.
“The impact he’s had and the influence he brings whenever he enters the room is huge.
“But then he’s also very good at maintaining personal connections with people,” he said.
Mr O’Connor said Harry has taken the time to meet with competitors from all the nations involved.
“It’s definitely not just the favouritism to the UK. He’s influential to everyone and it clearly means a lot for his presence to be here, and he’s made such a huge difference,” he said.
Harry founded the Invictus Games to aid the rehabilitation of injured or sick military personnel and veterans from across the globe, by giving them the challenge of competing in sporting events similar to the Paralympics.
Some 150 friends and family have joined competitors in The Hague to cheer on Team UK, supported by the Royal British Legion.
Harry and Meghan made their first public appearance together in Europe since quitting as senior working royals more than two years ago when they attended a reception at the games on Friday.