The name (The United States of America) is very generic and could mean several other countries, as Canada, Mexico and Brazil are also federations and are located on the American Continent.
It doesn't have a personal touch (like Uruguay and Paraguay, which resemble each other but also differentiate from each other clearly), it is merely a definition of a class of countries.
If the definition would be narrowed, for example, to "The United States of North America" then it could still be any of 3 countries and it still would be confusing.
It is somehow shameful for such a great country, with such personality, to have such a generic name.