Credit: Gustavo Caballero/Getty; Michael Kovac/FilmMagic

Well, there's now probably one name out of the running for Kim Kardashian and Kanye West's baby-to-be: Briseis. That's the moniker chosen by her ex Reggie Bush and his fiancee Lilit Avagyan for their little girl, the NFL star confirmed to  Us Weekly at the Work Out With Reggie Bush And Mission Athletecare event in NYC Thursday, April 16. (Bush was on hand to launch the Mission Enduracool instant cooling collection, available at Sports Authority and Dick's Sporting Goods.)

As first revealed by Us, little Briseis was born May 6, and weighed in at 8 pounds, 9 ounces. "She's brand new. She's doing great," Bush told Us. "She's amazing. She;s so beautiful. I love her to death. It's just been an amazing experience so far so I'm very excited – just being a father."

Fatherhood itself is still sinking in for the Bush, who split with Kardashian back in 2010. "I look at [Briseis] and I can't believe she's mine. There's still that element of I can’t believe this came from me."

Bush has been spending some necessary time at training camp with the Lions, but baby and his wife-to-be are the priority. "When I'm with her, I want to spend time with her so I'm doing my best to make sure I'm home as much as possible."

As for his Armenian-born dancer love Avagyan, 25? "My love has always been strong for her, but I think it just grounds us more. Having a child now just grounds us more . . . She has the wisdom of a 35 year old. She's very mature for her age." The pair hope to wed "next summer," he revealed.

Bush is no longer in touch with Kardashian -- whose own baby-to-be with Kanye West is due in July. "I always wish her well. Always."