Bookmakers have already pegged Alice as the favourite for the new royal baby’s name.
Coral opened betting on what the Duke and Duchess of Cambridge will call their third child, and gave Alice odds of 7-1.
Arthur and Victoria are 10-1 joint second favourites, ahead of Alexandra and Albert, both 12-1.
The bookmakers have set the chance that Kate has twins at 4-1.
Coral spokesman David Stevens said: “Late last month we had to cut the odds on the royal couple announcing this news to 1-2 from 3-1, and that gamble has proved to be spot on.
“It’s cost us a few quid but we’ll be paying out with a smile after this good news.”
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He added: “Alice is the early favourite when it comes to the potential name of the royal new arrival, while Diana at 14-1 could prove popular with punters.”
Paddy Power also has Alice as the favourite at 8-1, with Arthur at 10-1 and Diana at 20-1.
A Paddy Power spokesman said: “Given the recent anniversary, there’ll be plenty of interest in the name Diana if the baby is a girl.”
William Hill has Alice as the 8-1 favourite, with Elizabeth and James both at 10-1. With US leader Donald Trump in charge of the White House, Donald is at 50-1.
Joe Crilly, William Hill spokesman, said: “Royal baby betting is big business and when Prince George was born, we took over £1 million. Turnover looks set to spike again.
“Most of the names towards the top of the betting are ones which have been popular the last two times around and we expect they will be again.”
William Hill set the odds of royal twins at 33-1.
“Last time around, twins was very heavily backed from 33-1 in to 10-1 and it would be no surprise to see the same thing happen this time,” said Mr Crilly.