The 23-year-old British singer confirmed as much Tuesday during a Twitter exchange with survivalist and television personality Bear Grylls.
"Great choice!" Grylls tweeted of the name. "Love & blessings to you guys as you start on the greatest adventure... @CherylOfficial @LiamPayne."
"@BearGrylls @CherylOfficial Thanks man hope he grows up with an ounce of your courage! Your a boss," Payne wrote in response.
The Sun reported Monday that Payne and Cole had chosen the unique name. Sources said the couple waited to pick a name until they spent time with their baby and found one that "suited" him.
"Cheryl and Liam wanted to get to know their baby before deciding on a name," an insider said. "They spent over a week getting to know him first."
"They love their little baby Bear Payne and are truly over the moon and loving being parents for the first time together," the source added.
Bear was born March 22. Payne later shared the news by posting a sweet photo and message on Instagram.
"I'm incredibly happy to welcome our new baby boy into the world, it's a moment that I will never forget for the rest of my life and my favourite memory I have so far," he wrote. "I feel very blessed."