There are two countries with the words "United States" in the name: the USA and Mexico. There is only one country with the word "America" in it. So "America" as an informal name for the USA is appropriate.
Personally I don’t care what you call us in other languages, but in English it’s just “Americans”.
There are two continents, "North America" and "South America". To refer to the whole, you pluralize it as "the Americas".
Major places (and IMO it is a mark of the importance of a place) have different names in different languages. London does, Germany does, Japan does,....