The Duchess is due to give birth at some time in April.
WATCH: What are punters betting Harry and Meghan will name their baby?
The odds of the Sussexes giving their little one the name of Harry's late mother, Diana, now stand at 5/1.
Another front runner is Alice, after Queen Victoria's second daughter who, like Meghan, was a huge patron of women’s causes.
Victoria and Grace are also short odds on betting sites.
First time parents Harry and Meghan have previously said they want the gender of their baby to be a surprise.
Baby Sussex will be the eighth great-grandchild for Her Majesty Queen Elizabeth, following Prince William and Kate Middleton's children - Prince George, Princess Charlotte and Prince Louis - the daughters of Peter and Autumn Philips - Savannah and Isla - and the daughters of Zara and Mike Tindall, Mia and newborn Lena, who was christened last weekend.