California Code, Elections Code - ELEC § 2115

Whenever a voter, between the time of that person's last registration and the time for the closing of registration for any given election, has lawfully changed his or her surname, the voter shall reregister under the new or changed name. The voter shall make an additional statement at the time of reregistration, giving the name under which he or she was last registered.

This additional statement shall be given in the prior registration portion of the affidavit of registration before the affidavit is signed, and shall be deemed a part of the affidavit. Upon reregistration, the registration of the voter shall be immediately updated.