As you may have found out especially with the tabloids and magazines having all of these predictions on what Kim and Kanye named their baby, it came down to Kaidence Donda West.
Kim and Kanye did mention in one of their interviews that their daughter was going to have Kanye's mom's first name as the little girl's middle, but everybody was dying to know what was going to be the first name. At first MTV was thinking it was Emilee then there were other articles saying it was Kai, but most of the press have been confirming that it Kaidence. I really liked Kai, but Kaidence is good, too. It was questioned whether or not Kim was going to do the "K" name pattern like her mother, Kris Jenner, did with them, but she said she did have other options that weren't "K," but I guess she figured why not!
Again big congrats to Kanye and Kim!
Update (6/21/13): From what E! News is saying, Kanye and Kim named their baby North, but is going to call her Nori for short.