The name Maceo means "gift of God" and is the Spanish version of Matteo or Matthew, the celebrity news website noted.
Martinez's father is Spanish and his name is Robert.
Berry, 47, gave birth to her second child Saturday at Cedars Sinai Medical Center in Los Angeles.
The "Monster's Ball" Oscar winner also has a 5-year-old daughter, Nahla, with her ex-boyfriend Gabriel Aubry.
Berry and Martinez were married in France last July.