I've never seen a car, van or small truck (eg pickup) with the company name and such that's been banned from any of the NJ or NY "no commercial vehicles" roads. Is there really a difference between a bumper sticker with a commercial name on it as opposed to a larger one somewhere else on the vehicle? I doubt you'd have a problem, but I guess you'd have to check the DMV rules to know for sure.
BTW, congrats on your smart and welcome to the forum.