""The United States of America" is an odd name for a country, but it derives from the fact that there were 13 colonies who joined together to fight the British, and they all considered themselves to be independent sovereign states, but joined in a federation."

Further to LH's observation, when The United States of America was created it was, in fact, the only group of states in the Americas to be so united. In fact, there was no other independent country in the hemisphere then. Hence the name was appropriate.

Finally, if the South had won the Civil War, we would now be the Untied States of America...