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.