and even the time and day of birth.
The baby will be third in line to inherit the throne, meaning a King John II or Queen Anne II could be on the cards.
The William Hill firm's early favourites are Frances and John at 9/1, with Charles, George and Victoria 10/1, followed by Anne, Diana, Philip, Richard and Spencer at 12/1 and Henry, Mary and Sarah at 14/1.
Frances was Diana's middle name, while her father was John and the family surname is Spencer.
Elizabeth and William are both 16/1, while Catherine is 20/1.
Less regal-sounding names like Kevin, Wayne and Sharon all come in at 250/1.
Irish bookmakers Paddy Power have Mary, Victoria and John at 8/1, followed by Diana and Frances at 9/1, then Philip, Anne, Charles and George at 10/1. Sarah and Louis are 12/1.
Wallis, the name of the US divorcee that king Edward VIII gave up the throne for in 1936, is a 100/1 shot.
"We're pretty confident they're going to stay with a traditional name from within the family," Paddy Power spokesman Feilim Mac An Iomaire told AFP.
"We think that given, let's face it, they're not Lady Gaga but neither are they the generation of royals that went before them, they might not go too far off the wall."
William Hill are offering 10/11 on the sex of the baby, while twins is a 20/1 shot.
Paddy Power are offering a market on the godparents, with both William's brother Harry and Catherine's sister Pippa Middleton leading the way at evens.
The Irish firm is also taking bets on what time the baby will be born, and the baby's weight.
"Our traders seem pretty confident that's it's going to fall among the average. I don't think Kate will have too much strife," said Mac An Iomaire.
"Looking at the two of them we don't think there's enough stock in there to produce a giant."