Where do you start in changing a childs last name in CA?

I need to change my daughters last name. The non- custodial parent has never been in her life and she needs to have the same last name as me- she is 2 so she wont have to go through life with a name that doesn't match mine. I know I have to go to the court house, and have to pay- Is that it? I have full custody, so do I need to serve the non custodial parent papers and keep him in the loop? I believe that isn't necary but im not sure. Thanks!