Benicio del Toro and Kimberly Stewart welcomed their baby daughter on Sunday, and now a source has exclusively confirmed to ET that they've chosen the name Delilah.
The source also confirms that Benicio was at the hospital for the baby's birth on Sunday.
Last April, a rep for Benicio, 44, confirmed that the actor was the father of Kimberly's child, emphasizing that "Although [he and Kimberly] are not a couple, they are looking forward to the arrival of the baby." Kimberly, 32, is the daughter of Alana Stewart and rock legend Rod Stewart.
Benicio won an Academy Award for his role in Traffic in 2001.
Kimberly was engaged to Laguna Beach star Talan Torriero back in
2005 but the two called off their engagement two weeks later.