"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.