People.com: Naomi Watts and Liev Schreiber have revealed more details about their newborn son, starting with his name: Samuel Kai Schreiber.

Samuel - the couple's second child after year-old son Alexander Pete Schreiber - was born Saturday and weighed 7 lbs., 13 oz, the couple's rep tells PEOPLE.

"Both mom and baby are doing great," the rep says.

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