Speaking on 'The Ellen DeGeneres Show', she said: "I never would have guessed that would have been the name.
"But I was reading a book with my husband. I was three months pregnant and they said your baby is the size of an olive, and that was it. We never looked back."
Ellen then joked: "It could have been the size of a peanut or a grapefruit."
Drew replied: "It could have been. It was a lot fruit and vegetables."
The 'Going the Distance' star did consider a number of names, but as soon as they thought of Olive, they didn't deliberate anything else.
Drew explained: "We were shopping a few [names] as all people do who are so blessed to get to do this. And then once the light was shed, there was just no turning back."