Sharing the very first picture of his face on Instagram, the couple announced his name is Wave Set Cephus.

The rappers already share a three-year-old daughter named Kulture, but welcomed their son back in September.

He was pictured in a blue fur-trimmed parka and a blue beanie hat, teamed with huge diamond necklaces.

Cardi B, known for songs such as Bodak Yellow and WAP, captioned the photos with emojis of a dinosaur, a wave and a bear.

Meanwhile, 30-year-old Offset shared a picture of his son in the bath, still wearing necklaces, with the caption: "Wave Set Cephus".

In a tweet, Cardi B, whose real name is Belcalis Marlenis Almanzar, suggested that the name was her husband's idea.

"When Set suggested Wave, I was sold! That had to be his name," she wrote.

The message was accompanied by a video of her baby's large necklace, which spells out his name on a wave depicted in diamonds and a baby shark on a surfboard.

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Offset, real name Kiari Kendrell Cephus, is also father to daughter Kalea, seven, and sons Kody, seven, and Jordan, 12, from previous relationships.