British bookies firm Coral has slashed the odds on the name to 2-1 from 25-1 after receiving an unusually large flurry of bets on it.
Spokesman Simon Clare said Thursday the company had taken 10,000 bets on various names, but he was surprised to see about 2,000 pounds ($3,080) in bets on Alexandra in a matter of hours.
Rivals William Hill and Ladbrokes also have Alexandra as 2-1 favourite.
Earlier, Coral suspended bets on the baby being a girl. The royal couple say they don't know the gender, but last month the former Kate Middleton appeared to let slip that it was a girl.