Colin Jost Jokes About His Mom's Reaction to Baby Son Cosmo's Name: 'Is It Final?'

Colin Jost and Scarlett Johansson welcomed their first baby together, son Cosmo, they announced last month

Colin Jost says his mother wasn't instantly sold on his baby boy's moniker.

The Saturday Night Live star, 39, appeared on Late Night with Seth Meyers Thursday, joking about life with his son Cosmo, whose birth he announced last month. When asked about the inspiration for the name he and wife Scarlett Johansson chose, Jost said his mom threw out alternative options and variations on the name Cosmo at first.

"My family is very supportive always. My mom, I would say, was slightly thrown by it and didn't quite understand it. I don't know if she thought it was kind of like a hippie thing?" he said.

"She would call us, after three or four days, she'd be like, 'Cosmo...' And she'd be like, 'And, now, is it final? Like, did you submit the birth certificate?' And we're like, 'Oh, yeah, we did that at the hospital,'" said Jost. "She was like 'Oh okay, interesting. Because I was reading that there's also a name Cosimo with an "I" so that could also be an option. Maybe you call him Cosimo, that's his real name, but then you can call him still Cosmo.'"

After meeting more Cosmos in everyday life on Staten Island, his mom eventually warmed up to the name. "So then," he said, "she would call, and she would say, 'I met someone — they said their uncle's name is Cosmo, so it is okay.' And I was like, 'It's locked in.'"

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Last month, after PEOPLE confirmed that the pair welcomed their first baby together, Jost then gave more insight about their new family of four.

"Ok ok we had a baby. His name is Cosmo. We love him very much. Privacy would be greatly appreciated," he wrote on Instagram, then joking with his SNL costar Michael Che, "For all inquiries please contact our publicist @chethinks." He also added the hashtags: "#wegotawaywithitforalongtime" "#nokidspolicy" and "#weregoingtodisneyworld."

A source told PEOPLE at the time that Jost and Johansson — who is also mom to 7-year-old daughter Rose Dorothy — are "both so happy and madly in love with the baby."

"They wanted this child who will fit right into their lives since they already have her daughter," the source said. "They are an awesome couple, both talented, smart and clever. They will be the best parents. Colin is considerate and helpful in everyday life so adding one more to the mix should be fine. The baby is the best thing ever for both of them."