You can petition for a name change for the child but you must serve the father with the petition and he may file a response or objection.
The answers on this discussion board are general in nature and NOT intended as legal advice. Responding to questions does not constitute an attorney-client relationship. Always see a lawyer about your individual situation.
You must file a name-change petition at your local courthouse. The clerk should be able to provide you a packet, or sell you one at a nominal cost. It requires notice to both parents if the person whose name will be changed is a minor.
For instructions, you may find this book, http://www.nolo.com/products/how-to-change-your-name-in-california-NAME.html, or another book available at your local library, law library, or legal bookstore, helpful.