"Melanie spent a while deciding on the baby's name," a friend of the singer tells PEOPLE. "It was inspired by a number of things."
On Tuesday, Brown, who lives in Los Angeles, explained the name in a brief statement released through her London reps.
"Angel, as she was my little angel through my pregnancy," she said. "Iris, as it's my grandma's name, Murphy because he's the dad and Brown because I'm the mum!"
Angel Iris is the second child for the former Scary Spice. She has an 8-year-old daughter, Phoenix Chi, with her ex-husband, dancer Jimmy Gulzar.
In March, Murphy's new girlfriend, film producer Tracey Edmonds, told Chicago's Power 92 radio station of Murphy: "There'll be a paternity test and if it's his then he'll be responsible."