John Mulaney is taking fatherhood very seriously. At least according to him. But his pal Jimmy Kimmel appeared less than convinced on Monday, when Mulaney stopped by his late night show for a chat. During their conversation, Kimmel pointed out that Mulaney and his wife Olivia Munn welcomed their second child in September, a daughter that they named Méi June. "Her name is Méi," Kimmel observed. "And her middle name is June… Did you do that to be funny?" "No," Mulaney insisted, quipping, "I'm a professional comedian, so if I was going for funny, it might be a harder laugh than May next to June." He went on to explain that his daughter's name was actually intended to honor his mother-in-law. "Olivia's mom's name is Jung, so we were doing an Americanized tribute to her by naming her June," he shared. "Originally, our daughter was going to be named June." But plans changed when it occurred to the comedian that "June Mulaney sounds like John Mulaney" if someone "said [it] weird." He explained, "So we said 'How about Méi?' — which means plum in Chinese — and so she's Méi June." In response, Kimmel appeared mostly convinced that the pun was unintended and told Mulaney, "I'll accept that." Sign up for Entertainment Weekly's free daily newsletter to get breaking TV news, exclusive first looks, recaps, reviews, interviews with your favorite stars, and more. Mulaney and Munn, who also share 3-year-old son Malcolm, welcomed Méi to the family on Sep. 14, 2024 via gestational surrogate. The couple began dating in 2021 and wed in July 2024, months before their daughter's birth. Neither have shied away from gushing about their kids' progress, frequently sharing photos and sweet posts about their family on social media. During a recent visit to CBS Sunday Mornings, Mulaney emphasized that fatherhood has fully changed his outlook on life. "I'm in the world now that I'm a father. My head was my only home before that," he said. "When my son was born, the first thought I had was, I went, 'Oh, there you are.' And when my daughter was born, I had this – not to sound 'woo-woo' or anything – but when she was born, I went, 'Oh!'" He explained, "My thought was like, 'Oh, we've met before. I've collided with you some other time.' So, it's like these people came in that just, I don't know, make me like the world a lot more." Watch Mulaney's full conversation with Kimmel above.