Cal. CORP § 12311

(a) The names of all corporations formed under this part shall include “cooperative.” No corporation shall be formed under this part unless there is affixed or prefixed to its name some word or abbreviation which will indicate that it is a corporation, as distinguished from a natural person, a firm, or an unincorporated association.

(b) No person shall adopt or use the word “cooperative” or any abbreviation or derivation thereof, or any word similar thereto, as part of the name or designation under which it does business in this state, unless incorporated as provided in this part or unless incorporated as a nonprofit cooperative association under Chapter 1 (commencing with Section 54001) of Division 20 of the Food and Agricultural Code, as a stock cooperative, as defined in Section 11003.2 of the Business and Professions Code, as a limited-equity housing cooperative, as defined in Section 817 of the Civil Code, as a credit union or organization owned for the mutual benefit of credit unions, or under some other law of this state enabling it to do so. However, the foregoing prohibition shall be inapplicable to any credit union or organization owned for the mutual benefit of credit unions, any housing cooperative, the financing of which is insured, guaranteed, or provided, in whole or in part, by a public or statutorily chartered entity pursuant to a program created for housing cooperatives, a nonprofit corporation, a majority of whose membership is composed of cooperative corporations, or an academic institution that serves cooperative corporations.

(c) A domestic or foreign corporation or association which did business in this state under a name or designation including the word “cooperative” prior to September 19, 1939, and which conducts business on a cooperative basis substantially as set forth in this part, may continue to do business under that name or designation.

(d) Any person, firm, individual, partnership, trust, domestic corporation, foreign corporation, or association which did business in this state under a name or designation including the word “cooperative” prior to September 19, 1939, but which does not conduct business on a cooperative basis as contemplated by Section 12201 of this part, may continue to do business under that name or designation if the words “not organized under the law relating to cooperative corporations” are always placed immediately after the name or designation wherever it is used.

(e) Any foreign corporation, organized under and complying with the cooperative law of the state or other jurisdiction of its creation, may use the term “cooperative” in this state if it has complied with the laws of this state applicable to foreign corporations, insofar as those laws are applicable to it, and if it is doing business on a cooperative basis as contemplated by Section 12201.