Offset came up with the name Wave Set Cephus for his and Cardi B's son.
The couple welcomed their second child seven months ago but only announced his name last week and it was Migos rapper Offset, 30 - whose real name is Kiari Kendrell Cephus - that suggested the unusual name.
According to TMZ, Cardi, 29, loved Wave as soon as Offset suggested it but it was a struggle for them to decide on a middle name.
They originally considered Marley, in homage to Cardi's middle name, Marlenis, but Cardi did not like how Wave Marley Cephus flowed.
So, Offset - who is known as Set to his friends - suggested his nickname, which Cardi loved.
Cardi and Offset have been married since 2017 and the pair welcomed their first child Kulture back in 2018.
Cardi previously explained that they had gone through "a lot of sad things" when she made her firstborn known to the public, which is why they kept Wave under wraps for seven months.
She said: "We went through a lot of sad things when it comes to Kulture - terrible stuff that not even the older kids have ever been through. So many people will post mean, disgusting things, just to get a reaction from us. We want to protect our feelings, because we get very, very angry and upset."
'Open it Up' hitmaker Offset is also father to Joran, 12, and seven-year-olds Kody and Kalea from previous relationships and he explained that it is a "blessing " to be part of a blended family.
In a joint interview with Essence Magazine, he said: "It's a blessing to be able to have them all together, and to have a wife who's open and treats them as if they're her kids. It could be an issue, but I don't have to go through that, and that's beautiful."