None now, but the rules were previously different. Prior to 2018 when the new California Rules of Professional Conduct went into effect, a law firm was defined in Rule 1-100(B)(1) as: “(a) two or more lawyers whose activities constitute the practice of law, and who share its profits, expenses, and liabilities; or (b) a law corporation which employs more than one lawyer; or (c) a division, department, office, or group within a business entity, which includes more than one lawyer who performs legal services for the business entity; or (d) a publicly funded entity which employs more than one lawyer to perform legal services.” Pre-2018 California Rules of Professional Conduct.
In consequence, because of the two-lawyer minimum, solo practitioners could previously not use the designation “Law Firm”, instead, you would typically see “Law Office of Jane Doe”, etc.
This changed in November 2018 with the new Rules of Professional Conduct (Rule 1.0.1(c)), which now reads:
““Firm” or “law firm” means a law partnership; a professional law corporation; a lawyer acting as a sole proprietorship; an association authorized to practice law; or lawyers employed in a legal services organization or in the legal department, division or office of a corporation, of a government organization, or of another organization.”
Accordingly, the designation “Law Firm” is now available to solo lawyers as well, bringing the use of designation in line with general understanding of the term: “A law firm is a business entity formed by one or more lawyers to engage in the practice of law.” Wikipedia.