Among the most favoured names for the royal baby, George is favourite at odds of 9/4 with James just trailing behind at 11/4.
Also among the top choices for those placing bets at the bookmaker are Alexander, Louis and Henry, Sky News reported.
Punters are also letting people place bets of 66/1 on Daniel, or 50/1 for Andrew - after the baby's great uncle.
Prince William and the Duchess of Cambridge are expected to follow tradition however, with most Royal infants having monikers that have been passed down through the generations.