Prince William has dropped the biggest hint yet about the name of his third child while paying tribute at an Anzac Day ceremony in London.

Speaking to guests, the Duke could be heard saying the new royal baby has a "strong name" and that Kate and the new prince were "very well" and "in good form, luckily".

"Sleeping's going reasonably well so far, so he's behaving himself, which is good news," he said.

The Duke met Sir Jerry Mateparae, New Zealand High Commissioner to the UK, and the Dean of Westminster, who joked about the eagerly anticipated name, saying: "Jerry would like it to be Jerry", news.com.au reported.

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Britain's Prince William and Kate, Duchess of Cambridge pose for a photo with their newborn baby son as they leave the Lindo wing at St Mary's Hospital in London. Photo / AP
Britain's Prince William and Kate, Duchess of Cambridge pose for a photo with their newborn baby son as they leave the Lindo wing at St Mary's Hospital in London. Photo / AP

Australian High Commissioner Alexander Downer also suggested Alexander, to which William said cryptically, "Funny you should say that. It's a good name," the Sun reports.

Alexander is one of the bookies' favourites, although not as strong as Albert and Arthur, which are favoured by punters. It's also one of Prince George's middle names, as he is called George Alexander Louis. Prince William's full name is William Arthur Philip Louis.

The father of three has said siblings Prince George and Princess Charlotte are "very happy ... delighted" with the new arrival.

During the Anzac ceremony, Meghan Markle was welcomed by Te Ataraiti Waretini from Ngati Ranana — the London Maori Club — with a traditional hongi, the soft pressing of noses and the sharing of each other's breath.

Prince William, Meghan Markle and Prince Harry at an Anzac Day service at Westminster Abbey. Photo / AP
Prince William, Meghan Markle and Prince Harry at an Anzac Day service at Westminster Abbey. Photo / AP

Waretini said about Meghan: "She was amazing. I'm not sure if it's her first time at a Maori ceremony but she did very very well.

"It was really lovely to meet her and share the breath of life and share our culture with her and Harry."

Anzac Day has been commemorated in London since the first anniversary of the Anzac landings at Gallipoli in 1916, when King George V attended a service at Westminster Abbey and more than 2000 Australian and New Zealand troops marched through the streets.

The name of the new royal baby has not been announced but is expected to be made public in the coming days.