Kimberly Stewart New mum ... Kimberly Stewart.
New parents Benicio del Toro and Kimberly Stewart plan to call their baby daughter Delilah, Entertainment Tonight reports.
Stewart gave birth on Sunday at a Los Angeles hospital with her rock star father Rod Stwart and his wife Penny Lancaster by her side.
Del Toro and Stewart are no longer together but the Oscar-winning actor has confirmed that he is the father of the child.
Benicio del Toro Supportive ... Benicio del Toro.
When the pregnancy was announced last April, del Toro's representative said that "although they're not a couple, they are looking forward to the arrival of the baby."
Meanwhile, grandfather Rod is overjoyed at the expansion of his family, telling People.com, "My joy is indescribable."
In 2001, Del Toro won the Academy Award for Best Supporting Actor for his role in Steven Soderbergh's drug war epic Traffic.
Kimberly Stewart is best-known for her modelling work.
WENN and smh.com.au