Rebecca Gayheart and Eric Dane
03/10/2010 at 05:00 PM EST
Eric Dane and Rebecca Gayheart spent a bit of private time getting to know their newborn daughter before revealing the little one's name.
Now they tell PEOPLE exclusively their bundle of joy is Billie Beatrice.
The Grey's Anatomy
star, 37, and Gayheart, 38, welcomed their daughter
earlier this month.
Dane previously said his wife wanted to "wait to see [the baby]" before picking a name. "You want to make sure that the name sticks."
– Blaine Zuckerman