The 29-year-old reality TV star insists it would be ''too much responsibility'' if he was told the moniker of Kim's newborn tot with Kanye West and says he will only go to meet the new arrival when his step-sister Kim and Kanye are ready for visitors.
Speaking on Ryan Seacrest's KIIS-FM radio show, he said: ''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.
''You know, I don't know the name. I don't want to know! There's too much responsibility - don't tell me!''
Brody recently joined reality TV show 'Keeping Up With The Kardashians', which stars his father Bruce Jenner and his extended family and says it has helped him repair his fractured relationship with his dad.
He said: ''If I can go out there and show other people who maybe have relationship issues not only with their father, but with their mother or brother or sister, and just kind of reach out...you know, life is too short.
''[My relationship with Bruce] hindered my relationship with my little sisters [Kendall and Kylie Jenner, Bruce's daughters with Kim's mother Kris Jenner]. Growing up, I didn't get to see them as much because of the fact that I didn't get to see my dad as much, but now everyday it grows, and it's getting better and better.''