You might be asking a broader question than simply asking for the method for obtaining permission to reserve a name for a corporation or LLC. You may wish to discuss this subject with an attorney licensed in California, and possibly with trademark/servicemark experience in addition to corporate and business formation expertise.
The process of selecting a name which is sufficiently different or unique for registration with one of the secretary's of state is a slightly different question from doing the due diligence to insure the proposed name (including a fictitious name filing in multiple states where your company might do business) is: (A) viable for common law or state and federal trademark protection; or (B) not likely to cause undue confusion with other businesses in the jurisdictions where your company will do business; or (c) not likely to give rise to an infringement action under state or federal trademark laws. And this is just a start of the careful considerations advisable in selecting a business or tradename.
So, be sure you are not lumping together a number of legal issues and concerns into the process of simply creating your entity. Best of luck to you in your new business endeavors.
Note: This Answer and any information contained in this answer is not intended to be treated as legal advice; And, this posting does not create an attorney-client relationship or privilege of any kind.