Paris Hilton and her husband, Carter Reum, welcomed their baby boy last month via surrogate. The media star shared a very sweet Instagram post confirming the news that she’s a mama in a post dated January 25.

Today, the proud mom shared the first photos of her sweet baby boy—and shared his name publicly for the first time!

“Baby Phoenix. Our whole entire world,” she captioned the pair of professional photos of her family.

“It’s always been my dream to be a mother and I’m so happy that Carter and I found each other,” the new mama confirmed to PEOPLE in January. “We are so excited to start our family together and our hearts are exploding with love for our baby boy.”

Related: Chrissy Teigen shares first photo of her new baby girl—and her name is BEAUTIFUL

In the Instagram post she shared last month, Hilton posted a close-up photo of the teeny little baby boy baby gripping her thumb. “You are already loved beyond words 💙,” she wrote.

Hilton has always been open about her desire to become a mother. In an interview with PEOPLE just last month, she said that she and her husband began IVF during the pandemic.

Related: Rebel Wilson says she felt ‘disconnected’ while using a surrogate to carry her child

“We started going and doing it like a few months in because the world was shut down,” she said. “We knew we wanted to start a family, and I was like, ‘This is perfect timing. Usually, I’m on a plane 250 days out of the year, and let’s just get all of the eggs stocked and ready,’ and we have tons of them just waiting.”

Congratulations to the new mom and dad! We can’t wait to see more of him!