(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.
Source:
Section 1747.81, https://leginfo.legislature.ca.gov/faces/codes_displaySection.xhtml?lawCode=CIV§ionNum=1747.81..