Naming a baby is one of the biggest decisions new parents have to make, so it makes sense that Kim Kardashian West and Kanye West are taking their time choosing a name for their new son.

A day after their second child was born, the star couple still haven’t chosen his first name — or, at least, they aren’t sharing it yet — a source told .

The pair took almost a week to name daughter North, 2, and, shortly before her son’s arrival, Kardashian West told PEOPLE that they still didn’t have a name picked out. However, the source did say that Kardashian West reportedly told people at the hospital that she was going to use her late father’s name — Robert — for the child’s middle name.

“It’s like the last thing Kanye and I did when North was born,” she shared. “We didn’t name her for like seven days. I feel like it will just come to us.”

A source close to West also told PEOPLE that they hadn’t shared the new baby’s name yet.

“He never said anything about the name. Even if they had one picked out, he wasn’t going to share it. He doesn’t believe in telling anyone the name until the baby is born.”

The first source also reveals that Kardashian West did not have a C-section to deliver her baby, which was surely a relief.

After she learned that her baby was breech, the reality star wrote on her website and app that she was hoping to avoid delivering via C-section.

“Obviously, if it’s an emergency and for the safety of my son, I will get a C-section — but if I don’t need one, I’d rather not,” Kardashian West wrote.

The new mom had plenty of support throughout the delivery: Most of herfamily members stopped by the hospital on Saturday to deliver gifts and see their newest addition. And, the source says, older sister Kourtney, who has three children of her own and to whom Kardashian West has said she often turns to for pregnancy advice, stayed with her sister throughout her labor.