N.J. Stat. § 26:8-40.11
Whenever the mother of a child born out of wedlock, who has the same surname as the mother, and who has no presumed natural father pursuant to the "New Jersey Parentage Act," P.L. 1983, c.17 (C.9:17-38 et seq.), or the presumed father does not oppose the name change, marries a person who is not the father of said child, the surname of said child may be changed to the surname of the husband of the mother by submitting proof of such marriage to the State Registrar of Vital Statistics or to any local registrar of vital statistics, accompanied by a declaration, signed by said mother and her husband and acknowledged or proved in the manner required by law for deeds to real estate, setting forth that they desire the surname of said child to be changed to that of the husband of said mother and a declaration signed by the presumed father setting forth his approval of the name change. Upon the receipt of such proof and declarations, the surname of said child shall be so changed and the State Registrar and any local registrar of vital statistics is authorized to accept from the said mother and her husband a correction or amendment to the original birth record, giving the child the said husband's surname. Any declaration submitted to the State Registrar or to any local registrar pursuant to this section shall be filed with the original birth record of said child.
N.J.S. § 26:8-40.11