"Both mom and baby are doing great," a rep says after the birth of the 7-lb., 13-oz. boy

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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.

Reporting by LIZA HAMM