And no, "America" is not a pair of continents in standard usage -- that's "the Americas" you're probably thinking of (plural and with the definite article). Which is a rare term to come across, essentially unused in regular conversation, reserved for some highly specific contexts.
And I'm saying that companies being able to name themselves after political regions is absurd. How is that fair? I don't get to name my company "Google Bank" (and make it seem falsely associated with Google), so why should I get to name my company "New York Bank" (and make it seem falsely associated with New York)?
I do agree though that it is not so ambiguous really in the case of America, the Americas, North America, and South America—because there isn’t a singular “America” continent to refer to (unless we want to dip into the nightmare that is counting and naming the continents; Europe is a subcontinent, I’ll happily die on that hill). But “American” seems a little ambiguous, what else should we call somebody from the Americas, if we want to refer to them in that context? Nobody would say “An Americasian.”
If we want to refer to the continent we’ll just say North America.
If my name were “Bob of Idaho”, nobody would think Idaho meant only me. They would simply know I lived there.
Yes the United States are in the Americas, but it isn’t the entirety of them!
We have no more right to call ourselves “American” than Chileans do!
So in American English, at least, using it the way we do causes no real trouble.
What if you change your name to John New York then named the company after yourself, is that bad?
Because it equally associates it with the other millions of people there.
> What if you change your name to John New York then named the company after yourself, is that bad?
Yes. And it's not like you can change your name to John Disney and then start branding all sorts of things Disney.
I don't really get how you think a company using the name of the country is wrong but somehow a country appropriating the name of the continent is just fine?
> But in other countries we say-
Other countries exist?
It is sort of irrelevant what other countries call America or if they divide up the continents differently. Other languages name things differently.