1. Minor Name Change with Both Parents Filing
Follow the same process as for an adult name change, but make 3 copies of everything. Make 4 copies if publication is necessary.
2. Minor Name Change with One Parent Filing
a. Serve the other parent with forms NC-100, NC-110, and NC-120.
b. Complete and file form NC-121 Proof of Service of Order to Show Cause.
"You will have to pay a filing fee. Find out how much the filing fee is for a first petition
(sometimes called a “first appearance” or “first papers”). If you cannot afford the fee, you can ask for a fee waiver." From the California Courts website.
"Important: If you are changing your child's name and your child is in the State Witness Program or in the address confidentiality program and you are changing his or her name to avoid domestic violence, stalking, or human trafficking, or your child is a victim of sexual assault and you are asking for the name change on his or her behalf, you may keep the name change process confidential. Make sure you explain in the Attachment to Petition for Change of Name (Form NC-110) because it will affect the steps you have to follow to change your child's name. In these cases there is no fee for the petition if it is only for the child. You can find out more on item 7 of Form NC-100-INFO and on the Information Sheet for Name Change Proceedings Under Address Confidentiality Program (Safe at Home) (Form NC-400-INFO). If you want the process to be confidential, you must attach a Confidential Cover Sheet (Form NC-400) at the front of all your filed documents. If you are not sure what to do, talk to a lawyer or your court's self-help center." From here.
3. Minor Name Change by Guardian
a. Follow the same process as for an adult name change, and in addition use forms NC-110G Declaration of Guardian for Change of Name and NC-130G Decree Changing Name of Minor (By Guardian).
b. Make 4 copies of everything, or 5 copies if publishing.
c. Serve both parents with forms NC-100, NC-110, NC-110G and NC-120.