Halle Berry and Olivier Martinez Are Keeping Their New Baby’s Name a Secret – for Now

Halle Berry and Olivier Martinez


updated 10/07/2013 AT 1:00 PM ET

originally published 10/07/2013 AT 3:00 PM ET

Halle Berry and Olivier Martinez have picked out a name for their baby boy, who was born on Saturday in L.A., but fans will have to wait to find it out.

A source close to Martinez tells PEOPLE that the couple, who married in France in July, “have decided on a name that’s great in both the U.S. and France.”

Berry, 47 – who already has a daughter, Nahla, 5, with her ex Gabriel Aubry – and Martinez, who she met on the set of Dark Tide in 2010, “picked out a name for the baby months ago.”

According to the source, Martinez mentioned Christian as a possible name earlier this summer, but the actor, 47, says he and Halle want to keep the final decision a secret for now.

When Nahla was born in 2008, Berry admitted that they didn’t pick a name until she was born.

“For us it was hard to name the most important person in our life until we met her,” she said at the time.

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