The 34-year-old actress and husband Peter Sarsgaard welcomed their second daughter - a sibling for five-year-old daughter Ramona - into the world - into the world on April 19 and have named her Gloria Ray, according to US Weekly.
Maggie - who gave birth in New York - kept the pregnancy under wraps until her second trimester but previously admitted she found it difficult to keep her news quiet.
She explained: "I find it difficult to pretend you`re not pregnant, which I had to do. I didn`t let anyone know until three and a half months this time. I went to film festivals. I`m throwing up in the bathroom and having to keep pretzels in my purse, and having to fit into dresses."
Peter recently revealed he and Maggie were thrilled to know the gender of the baby as it gave them a chance to try out names before she was born.
He said: "It`s the nice thing about knowing the gender of a child; you don`t have to call it `it,` which gets really weird after seven months in. So we`ve been trying out a few names, but nothing solid."