(CNN) — Paris Hilton has shared the name of her newborn son.

On her “This is Paris” podcast this week, the reality star said she named her son Phoenix and that not even her mother, Kathy Hilton, or sister, Nicky Hilton Rothschild, had been told his name. On Thursday, Hilton also debuted the first picture of her son on Instagram.

Hilton and her husband Carter Reum revealed last month that they had welcomed a baby together via surrogate.

“For now we’ve just been keeping everything really private,” Hilton said on the podcast. “Not even my mom or my sister or my best friends — no one knew literally until he was over a week old, so it was really nice just to have that with Carter be our own journey together because I just feel that my life has been so public, and I’ve never really had anything just be mine.”

She added the reason she kept his name from her loved ones was because her life is so public and she knew it would somehow leak.

“If you tell one person, then they tell someone, and then all of a sudden it’s in TMZ or Page Six,” she said. “So Carter and I literally made a pact together that we would not tell anyone.”

Hilton, who also has a book coming out called “Paris: The Memoir,” read aloud from part of it, where she explains why the couple chose the name Phoenix.

“If all goes well, by the time you read this, Carter and I will have a baby boy,” Hilton read. “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 continued: “More important, 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.”

Paris Hilton reveals newborn son’s name