Prince William has broken his silence on the new royal baby – and even cheekily seemed to drop a hint at his name.

The 35-year-old attended his first engagement since the birth of his third child at Westminster Abbey’s Anzac Day service on Wednesday and responded to guests’ questions about the new arrival.

When Alexander Downer, the Australian High Commissioner, said that he thought his name would be a good choice, William teasingly replied: “Funny you should say that… It’s a good name.”

Meanwhile the Dean of Westminster joked that the New Zealand High Commissioner, Sir Jerry Mateparae, wanted the tot to be called Jerry when he introduced him to William.

“It’s a strong name, I have to say,” William responded with a smile.

Several guests seemed keen to ask the Prince – who attended the service with Prince Harry and Meghan Markle – about how Kate Middleton and the new member of the family are doing since the birth on Monday.

“They’re very well thanks,’ he explained, before adding that they’re “in good form, luckily”.

It sounds like the couple – who are also parents to Prince George, 4, and Princess Charlotte, 2 – are coping quite well sleep-wise too.

“Sleeping’s going reasonably well so far, so he’s behaving himself which is good news,” William revealed.

Prince William’s comments have sparked speculation that the little Prince could be called Alexander, though this is actually one of Prince George’s middle names.

Other monikers tipped by the bookies include Arthur, Albert, Phillip and James.

The couple welcomed their third baby at 11.01am on Monday after Kate, 36, had been admitted to hospital earlier that morning when she went into labour. He weighed in at 8lbs 7oz.

Later in the day William brought George and Charlotte to visit their new little brother at the Lindo Wing of London’s St Mary’s Hospital.

Within a couple of hours he and Kate gave the world a first glimpse of the tot when they appeared on the steps outside for photographs before leaving to travel home to Kensington Palace.