That is the only registration that you need. You must put the USCG registration number on the hull in a manner it cannot be removed(easily) This is usually done in the engine compartment where it is visible on inspection. I used stick on letters and covered them with 3m clear bra. You need to keep your registration paper on the boat for inspection. There are rules for sizing of lettering for name and port of call. Also required to have a "no oil discharge" plackard on the boat somewhere.
You also maybe responsible for State and Local taxes at place of mooring. I pay Kentucky property tax. Some don't need to pay, some don't pay, find out in OH.