New Jersey Statutes Title 2A. Administration of Civil and Criminal Justice 2A § 52-4

a. A certified copy of a judgment permitting a change of name;  or

b. A certification issued in connection with a naturalization proceeding authorized by Act of Congress that a change of name was permitted by decree or order of a court vested with jurisdiction to naturalize persons as citizens of the United States;  together with a request for correction of an existing record of the birth or marriage of the individual, the State Registrar of Vital Statistics or local registrar of vital statistics shall adjust the record or records to show the new name and the date and manner by which obtained.  When the request and such copy or certification are received by a local registrar, he shall forward them to the State Registrar after having adjusted his local record.

In the event the name of any child or children shall be permitted to be changed in the naturalization proceedings of the parent of such child or children, the certification of the parent's naturalization record or proceedings disclosing such change of name of such child or children shall be sufficient authority for the State Registrar of Vital Statistics or the local registrar, as the case may be, upon request, to correct the birth certificate or marriage certificate of such child or children in the same manner as provided for the correction of the parent's birth certificate or marriage certificate.  The fee to be paid a local registrar or the State Registrar for each birth certificate or for each marriage certificate so corrected shall be $2.00.  Any certified copy of a record changed as provided for in this chapter shall show the name at birth or marriage and the new name and date and manner by which obtained, but upon request shall show only the new name.