In the case Baby Sussex is a boy, Albert and Philip are the top names with James and Arthur as second favourites.
There's even bets placed on the exact time of birth, with an afternoon delivery between 12pm and 5.59pm is as the favourite.
The couple's first child is estimated to weigh between 2.7 and 10 kilos.
"Royal punters have spoken and if we're going with the majority, then Meghan will give birth to a baby girl named Diana on Tuesday afternoon, weighing a healthy 6lbs (2.7kilos) something!" said Alex Apati of Ladbrokes.