AceShowbiz -

Kim Kardashian and Kanye West reportedly have decided a name for their baby daughter. TMZ, which cited the baby's birth certificate from Cedars-Sinai hospital, revealed that the couple's first child would be called North West. A source told PEOPLE similar info.

Kim was said leaving the hospital four days after giving birth to her baby girl. According to TMZ, she currently stays in a private location while waiting for her new mansion to be ready. The "Keeping Up with the Kardashians" star is said to move to the $11 million mansion she purchased with Kanye in Bel Air next month.

Kim's step brother Brody Jenner recently praised the 32-year-old TV personality, saying that she would be an incredible mother to her child. "She's a wonderful human being. I've watched her with Penelope and Mason, Kourtney Kardashian's kids, and she is the best. She is one of the most incredible mothers to them, so I can only imagine what she's going to be when she has one to call her own," Brody told Digital Spy.

He continued gushing over his step-sister, "I commend her so much for doing what she's doing. She's airing everything of her life on the show - just put it all out there. She's pregnant, she's emotional, she's this and that, and then she's got to read all this stuff. It's a bummer that everybody has things to say about her, but she's going to be all good."

Brody, however, admitted that he had not met Kim and her baby. "It's so new, so I'm going to give her some time and then as soon as she's ready, I'll come see her," he said on Ryan Seacrest's radio show on Thursday.