Cal. Health and Safety Code § 1366

(a) No plan may use in its name, any of the words “insurance,” “casualty,” “surety,” “mutual,” or any other words descriptive of the insurance, casualty, or surety business or use any name similar to the name or description of any insurance or surety corporation doing business in this state unless such plan controls or is controlled by an entity licensed as an insurer pursuant to the provisions of the Insurance Code and the plan employs a name related to that of such controlled or controlling entity. (b) Section 2415 of the Business and Professions Code, pertaining to fictitious names, shall not apply to plans, except specialized health care service plans. (c) No plan or solicitor firm may adopt a name style that is deceptive, or one that could cause the public to believe the plan is affiliated with, or recommended by any governmental or private entity unless such affiliation or endorsement exists.