To a degree, i think you are asking the wrong question. An "in camera" review generally relates to a Judge reviewing a document in chambers that is being contested as evidence or as part of a discovery request.
What you are really asking is whether there is any authority to: (1) Hold a private hearing where the public is excluded; or (2) where the Judge can administratively approve the Petition without a hearing.
I think the latter would apply. Under teh California Code of Civil Procedure 1277, which relates to a name change, it states, as follows:
1277. (a) (1) If a proceeding for a change of name is ***** ***** the filing of a petition, except as provided in subdivisions (b), (c), and (e), the court shall thereupon make an order reciting the filing of the petition, the name of the person by whom it is filed, and the name proposed. The order shall direct all persons interested in the matter to appear before the court at a time and place specified, which shall be not less than 6 weeks nor more than 12 weeks from the time of making the order, unless the court orders a different time, to show cause why the application for change of name should not be granted. The order shall direct all persons interested in the matter to make known any objection that they may have to the granting of the petition for change of name by filing a written objection, which includes the reasons for the objection, with the court at least two court days before the matter is scheduled to be heard and by appearing in court at the hearing to show cause why the petition for change of name should not be granted. The order shall state that, if no written objection is timely filed, the court may grant the petition without a hearing. If the petition seeks to conform the petitioner's name to his or her gender identity and no objection is timely filed, the court shall grant the petition without a hearing.
Please see the last sentence of that statutory provision.