The University of California offers prviate lender lists as guides for students and parents, but you're free to use any lender of your choice.
Private loans (also known as alternative loans) can help to fill the gap between the cost of education and the amount of other financial aid offered. However, you should always maximize all other resources, including federal loans, which have lower interest rates and better loan terms.
Review The University of California Code of Conduct in Regard to Preferred Lender Arrangements (PDF)