I know, you don't intend on ever going back to land, but to exist in the real world of bureaucrats, tax collectors, and departments of motor vehicles you need to declare someplace on land as your domicile. I can just imagine some reading this grumbling about faceless bureaucrats and where they can shove their tax forms, but you simply can't fight this war and win. You will be pigeon-holed by the government even if they have to jam your square peg into a round hole against your will. I believe that most will be much happier in the long run if they round off their square corners in order to fit into the appropriate round holes unless you enjoy endlessly wrangling with bureaucrats, paying fines, and looking over your shoulder for the local sheriff.
By making your strange life as a fulltime cruiser look like anyone else's life when viewed from the office buildings in Washington, state capitols, and local government offices you will make your life much easier. Creating or maintaining a normal looking domicile is one key factor in doing this. Lots of mail forwarding services offer real street addresses that at first glance appear to offer the possibility of giving you something that looks like a real domicile, but they don't. The government and every financial service now requires you to prove your actual residential street address to access many services, like banking, driver's licenses, healthcare, etc. Almost everyone wants to have a driver's license, and in the USA the Real ID act means you must provide multiple proofs of a residential street address somewhere. In most cases they will not accept a commercial address like a UPS store, a mail forwarding company, or a Post Office box.
Since you will be on the move a lot you have no doubt thought about using a mail forwarding service. Many of these now offer mail scanning so you can review what has come in and decide what can be recycled, what needs to be forwarded, and maybe have a few things opened and scanned so you can simply download the mail without having to receive actual paper mail somehow. These services can be hugely helpful, but they mostly won't work to establish your domicile.
The key word is "mostly." A few services used by fulltime RVers and cruisers have been able to convince officialdom that they are legitimate addresses for domicile. The major ones often provide street addresses in Texas, South Dakota, or Florida and they have many loyal users. One major service used by many sailors is St. Brendan's Isle, providing an address in Green Cove Springs, Florida. I've used them in the past and their service is excellent. Prepare to spend $15-$30 per month for most services. Personally, I would only choose one of these services that is reasonably close to a place I might actually want to visit or bring my boat to. That eliminates Texas and South Dakota for me. I don't want to have to fly to South Dakota just to sort out a driver's license problem!
One way to use these services is to simply have your mail forwarded there using the US Postal Service, but keep in mind that certain things may not be forwardable--often mailings from election boards, tax collectors, and motor vehicle bureaus. In other words, some of your most important snail mail won't get to you via forwarding.
But, the best way to be a round peg is to "simply" find a real street address in a location you want and use that for everything important. Unfortunately, "simply" is not so simple for many fulltime cruisers. This real street address needs to be one where it is safe to receive valuable mail, is checked frequently by someone, won't change, and is not too costly. Obviously, you need to find someone you trust to manage this for you.
What are your options? For many of us, a trusted relative or friend is the first place to look. Who in your family or circle of friends is reliable, unlikely to move, and also takes an interest in your travels and lifestyle so would be willing to support it by lending their address to be your domicile? For long periods of fulltime liveaboard cruising I was lucky enough to be able to use my mother's or father's address for this purpose. I actually paid my mother a regular monthly fee to do this in order to enhance the idea that this was an important arrangement and to somewhat compensate her for the time involved. People are less likely to balk at doing something that is their job. One beauty of this was that my address was a place I would actually visit from time to time, making trips to a motor vehicle bureau or other office easier to manage. I would keep this in mind if you decide to use a commercial mail forwarding service. Make it someplace you visit anyway, or can get to easily when needed.
If a relative doesn't fit the bill, consider professionals you may use for other things. Possibly you have an accountant, or bookkeeper, or lawyer who takes an interest in your lifestyle and wouldn't mind receiving and occasionally opening and forwarding important mail for you. Be aware that you probably won't be able to use their business address as your residential address since automated systems will detect that--you need a real residential street address! But, someone like a bookkeeper is used to dealing with bureaucracy and government red tape that might be daunting for mom or dad.
An option that some cruisers use successfully is the street address of a marina where they dock or rent a mooring occasionally. Again, a business address may or may not be acceptable for some things like a driver's license, though I suspect you could convince some DMV offices to accept it if you brought a letter from the marina saying you liveaboard there. However, what if the marina sells, or the office manager changes, or maybe they just decide to stop accepting mail when you are on the other side of the world? I wouldn't use this option unless I had a good personal relationship with the people managing the marina. I've noticed piles of uncollected and unforwarded mail in many marinas.
Once you've found the reliable domicile address it is important to use it for every important piece of identifying mail or service: driver's license, U.S. Coast Guard Documentation, boat registration, car registration, insurance, taxes. When you're clearing into another country you want to have everything up-to-date, with matching addresses, and all looking totally ordinary so that nothing gets questioned. Having a regular street address that matches on all your documents helps. For example, I have seen cruisers have problems when the boats document doesn't match the hailing port on the stern or even sometimes the name on the boat. I myself have had problems with state taxes when the authorities assumed my hailing port meant my boat was located there, when in reality the boat had never been there.
This points out another reason you have to weigh all of your address options carefully. Some taxing jurisdictions (notably New York in my experience) are very aggressive at going after perceived tax cheats. Even though the Coast Guard doesn't require you to use a hailing port based on your home address it might make your life easier dealing with certain things like this. It is important to save things like marina receipts, haulout receipts, fuel receipts, etc. to prove where you have actually been if a taxing authority is claiming you owe. On the other hand, we have all seen hailing ports on transoms from places no boat has ever been because the area offers tax benefits. Again, this is a case of making yourself the round peg for the round holes that bureaucracy likes to see. For example, if your boat is actually based in Massachusetts a hailing port in Florida or Delaware might stick out like a sore thumb when the harbormaster is checking who is renting moorings. Certain ports of convenience, like Delaware hailing ports, are red flags that make you subject to even greater scrutiny from the tax man than you might deserve. Bottom line is to pay your taxes where they are due, and avoid the hassle and anxiety of trying to weasel your way out of them.
Sure, you can have non-critical mail sent someplace other than your domicile address, but you are probably better off just eliminating that mail if at all possible. Try to pair down what is sent to your domicile address to only the important stuff. However, no matter how hard you try, junk mail will end up going there eventually. This is another reason you need a trusted person who can review what is coming in and take appropriate action: credit card offers go in the trash or a pile for later forwarding, tax notices need an alert sent to you via email or other means, something like an actual credit card or bank card needs to be saved for when you are someplace you can receive actual snail mail safely.
Life on the water will be easier if you make yourself the round peg for the bureaucrats' round holes!