Cal. Gov. Code § 8213.6

If a notary public changes his or her name, the notary public shall complete an application for name change form and file that application with the Secretary of State. Information on this form shall be subject to the confidentiality provisions described in Section 8201.5. Upon approval of the name change form, the Secretary of State shall issue a commission that reflects the new name of the notary public. The term of the commission and commission number shall remain the same. Willful failure to notify the Secretary of State of a name change shall be punishable as an infraction by a fine of not more than five hundred dollars ($500).