In royal circles the tradition is for several: the Duke was christened William Arthur Philip Louis, while his brother Prince Harry is Henry Charles Albert David.
The couple have already shown they favour traditional choices when it comes to their eldest son who is George Alexander Louis.
So Charles, Philip and Thomas are likely to be good bets. James can almost certainly be ruled out as a first name because there are already two in their families - Kate's brother James Middleton and James, Viscount Severn, the six-year-old son of William's uncle Prince Edward. It might, however, feature as one of the middle names.
Michael may also be on their shortlist as a tribute to the Duchess' dad.
When it comes to girls names, Diana is an obvious choice for William's beloved mother. Elizabeth, Victoria and Mary may well be considered too because of their royal connections.
Alexandra is also a possibility given that it is one of the Queen's middle names. There have been two in the royal family: King Edward VII's charming consort and the cousin of the current Queen.
Meanwhile, the name Charlotte is relevant for the Middletons: it is the middle name of Kate's sister Pippa.
The royal family has had two Charlottes – the wife of George III and her granddaughter Princess Charlotte of Wales, who was clever, feisty and hugely popular. She's also a tragic heroine, having died young at 21 in childbirth.