I lived and worked in New Jersey and just recently bought a house on Florida. I will still be working out of New Jersey, so my question is.. Can I be a part-time resident of New Jersey or do I have to change everything to show my Florida address?

... do I have to change everything to show my Florida address?

What's everything?

You can continue to be a resident of New Jersey unless you choose to change your residence by, for example, registering to vote in Florida, or applying for a resident license of some sort.