Kimberly Stewart has named her daughter Delilah.
Her father - and proud granddad Rod Stewart - let slip the name during an interview with USA Today.
"I'm a grandfather now. I've been going around blabbing that for hours now," he said.
He told how the Stewart clan, including his third wife Penny Lancaster, Kimberly's brother Sean and mum Alana, visited the hospital to see the new addition.
"We had everyone at the hospital to help Kimberly. I won't say we always agree, but we get along," he added.
Actress and model Kimberly - Rod's daughter with first wife Alana - celebrated turning 32 by giving birth to the baby girl on August 21 in Los Angeles, and Rod described the arrival of his first grandchild as one of the happiest days of his life, telling People.com: "My joy is indescribable."
Delilah's father is Oscar-winning actor Benicio del Toro, who announced the news about the pregnancy in April through his spokesperson.
"Kimberly is pregnant. Benicio is the father and is very supportive. Although they are not a couple, they are looking forward to the arrival of the baby," his representative confirmed to People.com.