Kimberly Stewart has named her daughter Delilah Genoveva Stewart Del Toro.

The model gave birth toward the end of last month and has given the baby both her surname and that of the father, actor Benicio Del Toro, whom she is no longer with.

The birth certificate, seen by E! news, also confirms the baby is called Delilah, as speculated after her father, singer Rod Stewart, started singing the name after announcing he had become a grandfather.

Rod – who was at the Los Angeles hospital when Kimberly gave birth – said: "I'm a grandfather now. I've been going around blabbing that out for hours now."

The 66-year-old rocker has also previously said: "I've been waiting to become a grandfather for so long - that and getting my bus pass - the two things I was looking forward to getting."

In April Benicio's representative, Robin Baum, confirmed Kimberly was pregnant with the 44-year-old actor's baby.

Robin said: "Benicio is the father and very supportive. Although [he and Kimberly] are not a couple, they are looking forward to the arrival of the baby."