As for what the name means, Paris shared the significance of the moniker. "Phoenix has a few good pop culture reference points, but more importantly it’s a bird that flames out and then rises from the ashes to fly again," she said. "I want my son to grow up knowing that triumph and disaster go around and come around throughout our lives, and that this should give us great hope for the future." The heiress turned TV star turned DJ ended the post by saying: "Carter and I are so proud to welcome him into the world."