The 8-1 favourite at the moment is 'Victoria', and according to Express.co.uk it has been the most popular name since the couple announced they were expecting.
Albert is the leading contender for boys name at the shortest price of 10-1 in the betting, followed closely by Diana and Philip both at 12-1 and then Alice and Arthur at 14-1.
A spokesperson from bookmaker Coral John Hill said: "Victoria has been the most popular name in our Royal baby betting by some distance therefore it is the clear favourite ahead of Albert, Diana and Philip."
Queen Victoria is one of Britain's most famous monarchs and is the 10th longest reigning monarch of all time.