May 18, 2018 11:50 AM

Sorry, Stephen Colbert — you’ve been eliminated from Chrissy Teigen‘s name game.

The model and new mom of two had fun on Twitter Thursday, joking with Colbert’s late-night show’s Twitter account about how there was one problem with naming her newborn son after the host.

“Congratulations @chrissyteigen! If you haven’t picked out a name yet may we suggest Stephen? #LSSC 👶🍼,” The Late Show with Stephen Colbert tweeted, sharing a GIF from Teigen’s 2016 appearance on the show — which was shortly before she gave birth to daughter Luna Simone, now 2.

Replied Teigen, 32, referencing husband John Legend‘s given last name, “But then he’d be Stephen Stephens!”

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Chrissy Teigen and Stephen Colbert
Andrew H. Walker/REX/Shutterstock

RELATED: Chrissy Teigen Spent the Days Leading Up to Son’s Arrival Doing Something She “Never Does”

During Teigen’s 2016 appearance on The Late Show, she taught Colbert how to prepare a dish from her now-best-selling cookbook Cravings and admitted to the host that she and Legend, 39, change their choice for their baby’s name “all the time.” (“Stephen’s a beautiful name,” Colbert joked.)

The then-mom-to-be revealed that she had run her top pick by President Barack Obama, who gave his seal of approval, but Teigen wasn’t convinced — so on Colbert’s encouragement, she whispered it into his ear.

“I love that,” said the host, joking, “To hell with Barack Obama, you go with that.”

Chrissy Teigen and John Legend
Stefanie Keenan/Getty

RELATED VIDEO: Chrissy Teigen Says She’s “Over” Being Pregnant: I “Wanna Hold My Boy”

The couple announced the arrival of their second child on social media late Wednesday, with the Lip Sync Battle host tweeting, “Somebody’s herrrrrrre!” along with baby bottle and high-five smiley emojis.

On Thursday, a source told PEOPLE, “Chrissy has been baking — she never does — and taking it easy in the days leading up to the birth. She hasn’t been working out.”

Of Teigen’s demeanor, the insider explained, “She’s been in a great mood and is her usual happy, humorous self. She’s been super upbeat and just excited about welcoming her son.”

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