>No, I don't see how you think it's opposite.
Because you're misunderstanding the issue at hand.
Greece and Macedonia aren't having an abstract argument over sets. As the article explains, Greece has two specific objections to its neighbor using the name Macedonia: that the name (and certain actions) are thinly-disguised territorial claims against its own province of Macedonia, and are an attempt to lay lay claim to the historical/cultural legacy of the ancient Greeks.
This is why the US situation is the opposite, because the US as a separate nation predates all of the other nations you mentioned in the Americas. It therefore can't have been claiming territory of other neighboring states because there weren't any, nor were they claiming anyone's cultural legacy (except arguably the natives, but that's a charge that can be brought against every modern nation in the Americas).
It might help to recall that after the American Revolution the 13 colonies became 13 separate sovereign states that would only come together as a single nation in 1789 with the adoption of the U.S. Constitution. The new nation was a union of all then-extant states on an American continent, hence the United States of America. That other independent nations eventually came to be in the Americas has no bearing on what America chose to call itself at the time of its founding.