Pamela Redmond Satran, co-creator of baby name website Nameberry, predicts the pair will pay tribute to the 33-year-old royals late mother, Diana, if it's a girl.
Satran told Glamour, 'Diana is of course Harry's mother's name and the people's top choice for Meghan and Harry's daughter.'
'William and Kate broke some royal ice when they used Diana for one of Princess Charlotte's middle names, but Harry and Meghan could take that one step further by using Diana as a first name.
'Diana is the name of the Roman goddess of the moon and the hunt. Her Greek equivalent is Artemis, which be an alternative choice.'
Satran also picked out Eleanor and Sophia, as both names have ties to American and British culture.
If the couple are to have a boy, Satran believes Alvin is a good choice, as that is the name of Meghan's grandfather on her mother's side.
Other potential boys names include Arthur and Jams, which were both speculated for the Duke and Duchess of Cambridge's third son, Prince Louis.
Satran believes these names are still very much possible if another royal baby were to arrive.