Earlier this week, a rep for the Good American co-founder, 38, told PEOPLE that Kardashian and Tristan Thompson –– who split in January –– welcomed their second baby together via surrogate.

Now, a source tells PEOPLE that the proud mom is holding off on naming her bundle of joy until she knows for sure what she wants his moniker to be.

"Khloé is on cloud nine. Getting a sibling for True has been such a journey. She is very excited to be a mom again," the insider says. "She really wanted a baby boy."

"Khloé hasn't shared a name yet," adds the source. "She is taking her time with the name. She wants it to be just right."

Tristan Thompson/Instagram Khloé Kardashian and Tristan Thompson with True

Last month, it was revealed that Kardashian and Thompson, 31, were having a second child together. The exes are already parents to 4-year-old daughter True Thompson.

"We can confirm True will have a sibling who was conceived in November," a representative previously told PEOPLE. "Khloé is incredibly grateful to the extraordinary surrogate for such a beautiful blessing. We'd like to ask for kindness and privacy so that Khloe can focus on her family."

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Mandatory Credit: Photo by Frank Micelotta/Shutterstock (12988517d) Khloe Kardashian Hulu's 'The Kardashians' FYC Event, Hollywood, California, USA - 15 Jun 2022 Wearing Narciso Rodriguez, Shoes By Gianvito Rossi

Frank Micelotta/Shutterstock Khloé Kardashian

Kardashian and Thompson started dating in 2016 and welcomed daughter True in 2018. They split in June 2021 before reuniting. Kardashian then ended her romantic relationship with the NBA player in January of this year.

Thompson is also dad to son Prince, 5, with ex Jordan Craig and son Theo, 8 months, with Maralee Nichols.

Kardashian's decision to hold off naming her new baby right away comes about after sister Kylie Jenner faced a naming dilemma with her own secondborn earlier this year.

After giving birth to a baby boy in February, Jenner, 24, and Travis Scott shared a post on her Instagram Story a month later, revealing that their child would no longer go by the name of Wolf, the moniker he was originally given.

"FYI our sons [sic] name isn't Wolf anymore," Kylie wrote at the time, referencing her second child with Scott, 31.

"We just really didn't feel like it was him. Just wanted to share because I keep seeing Wolf everywhere," she added, along with a prayer hands emoji.

The mom of two has still not announced her baby's new name, or whether his middle name Jacques was also changed.