You are already loved beyond words," she shared at the time in a post on Instagram.

Speaking on her iHeartRadio podcast, This Is Paris, the new mom revealed she'd already decided on the name of her son, 10 years ago, in fact.

She shared while reading an excerpt from her upcoming tell-all, Paris: The Memoir, expected in March: "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.

"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."

"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."

Phoenix's full name is Phoenix Barron Hilton Reum – Barron is a tribute to the star's grandfather, a "mentor" to her