Registering flatbed trailer in NJ

Hello to all

I currently have a truck which is registered under a relative's name, I have been running local power only for quite some time..all under his company. A week ago I bought a flatbed trailer which I plan to run under this relative's MC# as well.

My question is, does the trailer need to be under my relative's name in order to get registered under his company or can it be under my name and just add it to his company's insurance?

Also, is there any special paperwork I need to bring into motor vehicle in order to legally register the flatbed, etc...? This is the first time I've bought a trailer.