New Jersey evaluates a parent's request for a change of surname under a best interest standard. See Gubernat v. Deremer, 140 N.J. 120, 141-42, 657 A.2d 856 (1995). Factors to be considered by the court include "the length of time that the child has used one surname, the identification of the child as a member or part of a family unit, the potential anxiety, embarrassment, or discomfort the child might experience if the child bears a surname different from the custodial parent, and any preferences the child might express, assuming the child possesses sufficient maturity to express a relevant preference."
Thus, to change the child's name you would have to ask for that relief (you can normally do so as part of adjudicated paternity proceedings) and meet the burden of proof that the name change is in the child's best interest.

