The dilemma of what to call the latest addition to their family is something the Duke and Duchess of Cambridge will be wrestling with but Mary is the public's favourite moniker.
Punters have been betting that William and Kate will name their baby - which they think will be a girl - Mary, a name which has a long association with the British monarchy.
Bookmaker William Hill has made the name their 3-1 favourite followed by Alice 6-1 and Victoria 8-1, while Coral has Mary and Alice as their joint favoured monikers at 5-1, with Victoria next with odds of 8-1.
William's great-great grandmother, the wife of George V, was called Mary, a woman who the Prince of Wales still speaks of fondly, and Mary is one of the Queen's middle names.
Britain has seen two Marys on the throne - Mary I, known as Bloody Mary for her persecution of Protestants, and Mary II, who ruled jointly as monarch with her Dutch husband, William III.
Rupert Adams, from William Hill, said more than 90% of bets placed had been for female names: "The favourite is Mary but I cannot see it as it is massively over backed. Alice is good but personally I am all over Victoria - which makes good sense to me."
If William and Kate have a girl they may be considering naming her Alice which was the name of the Duke of Edinburgh's mother.
Princess Alice of Battenberg was born deaf but learned to speak and lip-read four languages, married Princess Andrew of Greece in 1903 and went on to establish an order of nuns and wore a habit to the Queen's coronation in 1953.
Her grandmother was another Princess Alice - the third child and second daughter of Queen Victoria - who lived in Germany after marrying Prince Louis of Hesse.
She was said to have had a warm heart and opened hospitals, championed women's causes, founded women's guilds and patronised women's unions. She died in 1878 when she was 35.
For boys names, William Hill has Albert, Arthur and Fred all at odds of 14-1, while Coral has Albert and Arthur at 12-1, and a number of names at 16-1 including Arthur, Fred and Philip.