CAL. CIV. CODE § 1747.81 : California Code - Section 1747.81

(a) If a card issuer has determined in the normal course of business that it will issue a card to a married woman, the card shall be issued bearing either the maiden name or married name of the woman, as the woman may direct.

(b) Card issuers may require that a married woman requesting a card in her maiden name open a new account in that name.