You might also have your father contact the Superior Court in Santa Cruz County and request his "Final Decree of Adoption". If he was a private adoption sometimes the birth name appears on this document.
California Search Website:
http://www.adoptionforums.com
http://www.adoptionchat.com
http://www.adoptionlists.com
http://www.adoption.com
http://www.adopting.org
http://www.adoptionregistry.com