“She wants it to be fair,” the source says

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

Mandatory Credit: Photo by Frank Micelotta/Shutterstock (12988517d) Khloe Kardashian Hulu’s ‘The Kardashians’ FYC Event, Hollywood, California, USA – June 15, 2022 wearing Narciso Rodriguez, Gianvito Rossi shoes

Frank Micelotta/Shutterstock Khloe Kardashian

Khloe Kardashian takes it day by day when it comes to naming her newborn baby boy.

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

Now, a source tells PEOPLE the proud mom is waiting to name her bundle of joy until she knows for sure what she wants her nickname to be.

“Khloé is on a little cloud. Having a sibling for True has been such a journey. She’s very excited to be a mom again,” the insider said. “She really wanted a baby boy.”

“Khloé hasn’t shared a name yet,” the source adds. “She takes her time with the name. She wants it to be right.”

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Khloe Kardashian and Tristan Thompson

Khloe Kardashian and Tristan Thompson

Tristan Thompson/Instagram Khloe Kardashian and Tristan Thompson with True

RELATED: Khloé Kardashian and Tristan Thompson welcome their second baby via surrogate

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

“We can confirm that True will have a sibling who was conceived in November,” a rep previously told PEOPLE. “Khloé is incredibly grateful to the amazing surrogate for such a beautiful blessing. We would like to ask for your kindness and privacy so Khloé can focus on her family.”

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

Thompson is also the father of a son Prince, 5, with his ex Jordan Craig and son Theo, 8 months, with Maralee Nichols.

RELATED VIDEO: True Thompson Looks Like She Grew Up Jet-Setting With Mom Khloé Kardashian: ‘My Little Lady’

Kardashian’s decision not to name her new baby right away comes after her sister Kylie Jenner faces a dilemma of naming with 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 through the wolf namethe nickname originally given to him.

“FYI our sons [sic] no longer Wolf,” Kylie wrote at the time, referring to her second child with Scott, 31.

“We really didn’t feel like it was him. Just wanted to share because I keep seeing Wolf everywhere,” she added, along with a praying hands emoji.

The mum-of-two still hasn’t announced her baby’s new name, or if her middle name Jacques has also been changed.

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