You should absolutely disclose everything on the naturalization application. Furthermore, you should change your driver's license and car registration so that you can provide proof that you have done so, and that you are living in NJ at the time of your naturalization interview. This is especially important if you do not have other documentation to demonstrate that you reside in NJ. The officer at your interview will need proof that you have been residing in NJ for at least three months prior to filing your application. Further, you will have to tell him/her why you didn't change your driver's license upon moving to NJ.
Please note that content of this reply does not constitute legal advice or create an Attorney/Client relationship in the absence of an agreement for legal services/retainer with my office. This is just a place to start in deciding what to ask your lawyer.