Does a client have a right to privacy protection if they are identified as a client by their attorney?

Upon such public disclosure of the attorney-client relationship, the client's privacy concerns regarding the fact of the consultation evaporate and there is no longer a basis for preventing the attorney from identifying the client. (See Satterlee v. Bliss (1869) 36 Cal. 489, 501.) However, until such a public disclosure occurs, the client's identity is itself a matter of privacy, subject to the protection against involuntary disclosure through compelled discovery against the attorney.