Paris Hilton is introducing the world to her baby boy.

On her iHeartRadio podcast This Is Paris, the new mom revealed the name she's given to her baby boy — Phoenix Barron Hilton Reum.

Hilton, 42, explained that she thought of the name 10 years ago, sharing the story while reading an excerpt from her upcoming memoir, Paris.

"If all goes well, by the time you read this, Carter and I will have a baby boy. We plan to name him Phoenix, a name that I decided on years ago when I was searching cities, countries and states on a map looking for something to go with Paris and London," she read.

"Phoenix has a few good pop culture reference points, but more importantly it's the bird that flames out and then rises from the ashes to fly again," she continued. "I want my son to grow up knowing that disaster and triumph go around and come around throughout our lives. And that this should give us great hope for the future."

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Later, she explained that the little one's middle name is a tribute to her late grandfather, Barron Hilton.

"He was always my mentor. I looked up to my grandfather so much, and we were so close, and I miss him every day," she explained. "So, I really wanted to honor him by having his name in my first son's name. So there you go. My beautiful baby boy's name is Phoenix Barron Hilton Reum."

Hilton began the podcast by raving over her new arrival and how special this time has been for her and her husband, who is already a dad to a daughter whom he shares with former reality star Laura Bellizzi.

"As you all know, Carter and I have been blessed with the arrival of our baby boy. He is such a precious angel, and we're over the moon, so in love with him. We're just so excited to start our family, and we can't wait for you to see him," the new mom shared.

"But for now, we've just been keeping everything really private. Not even my mom, my sisters, my best friend knew until he was over a week old," Hilton revealed. It was really nice to have that with Carter, be our own journey together. I just feel like my life has been so public, and I've never really had anything be just mine."

Later, Hilton added, "From the moment I laid eyes on him, my heart felt so full. I feel like my life is so complete now. I always wanted to be a mom."

"I'm so happy I found the perfect partner. Carter, he is such an angel and such an incredible father," she continued. "It's so cute seeing them together and I just love this baby so much. He's laying on my chest and looking up into my eyes, my heart just melts."

Hilton expressed her excitement for her next chapters with PEOPLE exclusively after welcoming her baby boy in January.

"It's always been my dream to be a mother and I'm so happy that Carter and I found each other," she told PEOPLE at the time. "We are so excited to start our family together and our hearts are exploding with love for our baby boy."

Sharing the joyful news on Instagram, Hilton posted a close-up photo of the baby gripping her thumb. "You are already loved beyond words 💙," she wrote.

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