Kim Kardashian and Kanye West have named their baby daughter North West -- or "Nori" for short, a source confirms to Us Weekly Credit: Kevin Mazur/Wire Image

Yep, it's true! Five days after Kim Kardashian and Kanye West welcomed a baby girl, a source close to the reality star, 32, confirms to Us Weekly that the bundle of joy has been named, as long rumored, North West. The source adds that the "birth certificate is out," and that the little girl, born five weeks early, has no middle name.

The first child for Kardashian and the rapper, 35, already has a nickname, the source adds: "They will call her Nori for short."

Indeed, midday on Thursday, a second insider told Us that rumors of the couple's baby being named with a "K" a la her mom, aunts Kourtney Kardashian and Khloe Kardashian, Kylie and Kendall Jenner and grandmother Kris Jenner, were false. (One prevalent rumor suggested that the baby was named Kaidence Donda West, taking her middle name from West's late mother Dr. Donda West.)

North was born ahead of schedule on June 15 at Cedars-Sinai Medical Center in Beverly Hills. "Everybody is doing great," the insider adds of the family.

"The baby is so sweet. Kanye is in love. Kim's real due date was July 12 -- Kanye's mom's birthday. That warmed his heart."