The 47-year-old actress, who already has a five-year-old daughter Nahla from her previous relationship, gave birth to a baby boy on October 5, reported Ace Showbiz.
"They chose it because it means gift from God. Olivier wanted to give a nod to his Spanish roots. They picked the name a while ago, they love it," a source said.
The middle name Robert was picked after the "SWAT" actor's Spanish father.
Berry and Martinez met for the first time on the set of "Dark Tide" in 2010 and got married in July this year.