N.J. Stat. § 19:31-13
Whenever the registrant after his or her original registration shall change his or her name due to marriage, divorce, or by judgment of court, the registrant shall in person or by mail submit to the commissioner of registration a written statement notifying the commissioner of the change, which statement shall take such form, and be printed on a postal card suitable for mailing of such design, as the Attorney General shall prescribe and shall be signed by the registrant. A registrant may complete the form online as provided by the Secretary of State. The commissioner, upon receipt of such a notice of change of name, shall revise accordingly the name of the registrant as it appears among the items of information concerning the registrant included on the registrant's registration forms, shall make a photographic copy of the notice of name change submitted by the registrant, and shall affix the original notice so submitted to the registrant's original registration form and the photographic copy of that notice to the registrant's duplicate registration record.
When notice of such change in name has not been received by or filed with the commissioner prior to the 21st day preceding any election, such person may be permitted to vote under the name under which the person was registered prior to that change at the first election following such change in name at which the person shall appear to vote, after signing the signature copy register with both the registered name and his or her new name. The commissioner shall then revise accordingly the name of the registrant as it appears on the registrant's registration forms, make a photographic copy of the notice, and affix the original and copy of the notice to the registrant's permanent registration forms as hereinabove prescribed.
N.J.S. § 19:31-13