Carey was promoting her new film Suffragette in New York, when she revealed her baby's name on the red carpet.
"Evelyn," she told Entertainment Tonight. "We just came up with it."
"We just came up with it," said Carey Mulligan
During an appearance on The Graham Norton Show on Friday, Carey confirmed that she had welcomed a little girl. The 30-year-old gave birth around three weeks ago and said that she is "enjoying" her new role as a mum.
News of the actress' arrival came to light last week when Carey made her return to the red carpet at the opening of the BFI London Film Festival, after months out of the public eye.
The Great Gatsby star was said to have missed the world premiere of her film in Telluride at the beginning of September because she was due to give birth any day.
The actress gave birth around a month ago
Carey never announced her pregnancy news, instead choosing to hide her growing baby bump in trapeze dresses and loose clothing for her public appearances. She made her last red carpet appearance in a striking oxblood Balenciaga gown at the Tony Awards in June, around the time that her pregnancy was revealed.
A Broadway source told Us Weekly at the time: "They weren't planning on announcing, but she hasn't stopped working. Everybody around her is being very supportive. The show ends soon and they're going back to England after."
The news comes just months after Carey confirmed she was ready to start a family with the Mumford and Sons rocker, telling The Mirror: "Yeah, definitely. But I don't think you can ever be worried about your career when it comes to stuff like that. You've got to have some perspective."