It does not, but whoever controlling those domains may have their own rules about who may use them, and terminate your account if they feel you've broken their rules.
One common rule is that you have to actually be a person or company in that location. I know that's true for .eu (which was real fun for brexit), probably for .uk, but I don't think it's a requirement for .us.
If you really want that name, I'd pick a non-ccTLD and pay a bit more.