Kylie Jenner to Share New Name of Son 'When She's Ready,' Felt Like Wolf 'Didn't Fit': Source

Kylie Jenner doesn't have a timeline in mind as to when she'll reveal the new name of her son.

Earlier this week, the 24-year-old posted an announcement to her Instagram Stories sharing that her son, whom she welcomed last month with Travis Scott, would no longer go by the name of Wolf.

A source tells PEOPLE that Jenner will "share his name when she's ready."

"Kylie and Travis liked Wolf, but after getting to know their son, they felt like the name didn't fit him. They wanted to choose the perfect name that they both loved," says a separate insider.

For more on Kylie Jenner and Travis Scott changing their son's name, listen below to our daily podcast on PEOPLE Every Day.

Jenner, who is also mom to 4-year-old daughter Stormi, has not disclosed whether her son's middle name Jacques is also being changed.

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Jenner's announcement on Monday came just hours after she premiered a new YouTube video dedicated to her newborn, titled To Our Son.

The sweet video featured footage from all along Jenner's second pregnancy journey, from when mom Kris Jenner found out the happy news, to her giraffe-themed baby shower, to the delivery room just before her baby boy was born. The video also included the first look at her son's nursery.

In the clip, Jenner recorded herself sitting in the hospital bed, cradling her baby bump as she prepared to welcome her child. The video then cut to audio of the moment the baby was born. "He's out," one of the doctors is heard saying. "Your son is here!"

"What's up boy! What's up big boy," Scott shouted proudly before the newborn is heard crying.

"To our son. February, 2, 2022. 8lbs 13oz," the video reads at the end on a title card.