Ownership Transfer

So long story short my parents purchased our 2009 Escape XLT last summer as a gift for my graduation from college and my full-time job offer. I signed the paperwork for the car with my father, but the Registration for the vehicle is under my parents (mom and dad) name. Now that I am 23 years old and am the only person who drives the vehicle (parents don't know how to drive) I would like the vehicle to be under my name.

This is where it gets confusing, I am living in Queens now, but moving to New Jersey in about 3 weeks. I am not sure if I will need to get the vehicle registered in NJ or have it registered in NY state where I grew up and my parents still live and is the address on my NY state license?

Any input is appreciated.