I have returned to the US from Europe and filed a declaration of domicile, registered my car, rented property, obtained state licenses, and work in Florida. I anticipate remaining in Florida for years to come, and intend to maintain Florida as my permanent residence. Do I need to terminate my residency with the state of NC? And if so, How?

No, you don't terminate a residency. You establish a new residence. That's where you live, vote, register vehicles. That's your LEGAL address.

You sort of drop out of view in your "old" State. You don't notify the "old" State that you've left.

Judy, Thanks for the answer.