Kim Kardashian and Kanye West
06/18/2013 at 08:00 AM EDT
Even though Kim Kardashian
and Kanye West
's bundle of joy decided to arrive earlier than planned
, the reality star didn't require a cesarean section to deliver her daughter, a source confirms to PEOPLE.
"She was admitted with medical complications and her doctor made the decision that her baby needed to be delivered. Kim had a natural birth," the source says. "If Kim would have had very serious complications, her doctor would have decided to do an emergency c-section instead."
As for the baby girl's
name, Kardashian, 32, has mentioned in the past that it will likely begin with a 'K,' but so far, she and West, 36, remain undecided, although a second source tells PEOPLE that they are close to a final decision.
"Kim is being very protective of the baby and she says there is no official name," the first source notes.