The model told host Jimmy Fallon on Thursday that Psalm wasn't her first choice for the baby, but that Kardashian settled on the name after discussing it for hours.
"She would not let me leave the house until we figured out a name," Jenner said. "And then ended up going with a name that I didn't even like, that I didn't care for as much."
"I think that they were all really beautiful, but I was kind of rooting for another name," Jenner continued.
Psalm West, who was born in May, is Kardashian's fourth child with her husband Kanye West. The couple are also parents to 6-year-old daughter North, 3-year-old son Saint, and 1-year-old daughter Chicago.
Jenner and Fallon also played a game of Pour It Out where they took turns giving answers to mysterious, personal questions. The game involves having to either announce what the question was or to take a shot.
Jenner and Fallon both admitted to answering which two celebrities they would want to set up with each other. Jenner said Brad Pitt and Rihanna while Fallon paired together Avengers stars Chris Evans and Brie Larson.
"Wouldn't that be the most gorgeous child?" Jenner said about bringing Pitt and Rihanna together.
Jenner, afterwards, said she was a huge fan of Pitt's, but actively avoided meeting the actor while he was attending one of Kanye's Sunday Service concerts.
"Isn't there a saying like 'Don't ever meet your superhero?'" she said. "I just like love him so much that I'm like... I'm just going to leave it at that."