There is no particular procedure based on death of a spouse. It would just follow the general name change process. I believe the forms are available on the NJ Court's website.
You can pick up forms from the courthouse, follow the instructions and fill them out; I believe there is a fee to change your name. Once you complete the forms, submit them to the courts and receive a hearing date to appear and have your name change.
Thanks! Your answer is awaiting moderation.