In the US it's just https://moversguide.usps.com/mgo/disclaimer?referral=UMOVE
And this isn't even "required".
It does mean that you'll get your old mail delivered to your old place forwarded to your new place while the other folks mailing you get their ducks in a row. And honestly I can't think of all the places that might mail me.
Even if the move process is frictionless, in most countries, it's just not a thing. You are "tied" to your family house or apartment, passed from generation to generation. Here, real estate is just a commodity.
The basic point is that most people in the US will want some permanent address where they can get mail etc. and is where they live from the perspective of official government documents. But they may not actually live there (and aren't required to).
In the US it matters too to some extent, eligibility for elections if you want to hold office, your tax burden for states that tax property and so on. But there's not a super official universal office you need to declare it at with lots of paperwork or validation outside of say the given situation it applies to. If I ran for office I'd provide my address and there you go, no complex validation, or if I wanted to pay lower taxes because it is my primary residence ... I just say that's where I live. Those given processes are left to validate it if they wish.
Bureaucracy is a strange thing. We get comfortable with what we know and we can't think of it any other way and it becomes a bit of a revelation when we realize maybe we don't have to do all that ...
It's often one of the main reasons why they ask you to register in other countries.
Compared to what seems like a big mess of telling only the post and hoping everyone will get the memo from them, telling the utility, my employer, family, and a few insurances that I moved (updating the info on the self-service site or sending support an email) seems like the better solution to me
For say sales tax like things if you buy something online the address you ship it to usually determines that. So no effort required there. In person if you're in TX you pay the TX sales tax (if they have one), if you are in NY you pay the NY sales tax.
As far as filing taxes for a year goes (income tax, property tax) you file taxes (or maybe you don't) and there you go. Filling taxes is largely a sort of declaration of what you say you did and owe. It's up to the state or feds to validate if they wish.
I've been moving almost once a year for the last few years just to try out new places and cities.