My question involves name change laws in the State of: California

So I just received my certificate of naturalization today and my daughter, age of 16, would like to change her name. I've searched online and saw that I have to go to court, but then today during the ceremony I heard that I can change her name at SSA within the two weeks after I receive the certificate of naturalization. Is this true? And if so, what are the steps that I have to do and what documents will I need?