How did we get the name for our nation United States of AMERICA being America the whole continent?

This question is placed on me every time I visit Mexico and I would like to properly answer .How did we get the name for our nation United States of AMERICA being America the whole continent?
because these states were the only united states on both the continents of America that were independent of a European power when we declared independence. Hence the name was original. Now Mexico and Canada (and many South American Countries) have states or divisions similar to the United States and are independent, but the USA was the original such country in the Western Hemisphere. And Besides Canada, I believe it is the only country that came together from vastly different colonies, which were in them selves self governing of local affairs before the revolution. Canada is similar, but Mexico was one territory I believe, though I am not a Mexican Historian so could not tell you otherwise on that point.How did we get the name for our nation United States of AMERICA being America the whole continent?
The Articles of Confederation,





Article I








To all to whom these Presents shall come, we the undersigned Delegates of the States affixed to our Names send greeting.





Articles of Confederation and perpetual Union between the states of New Hampshire, Massachusetts-bay Rhode Island and Providence Plantations, Connecticut, New York, New Jersey, Pennsylvania, Delaware, Maryland, Virginia, North Carolina, South Carolina and Georgia.





I.


The Stile of this Confederacy shall be





';The United States of America';.
Like Ashley said, America is just the name of the continent. Because ours is the biggest (and arguably most important/powerful) of the three major countries in North America, when people say ';America,'; they commonly mean the USA -- right or wrong!





';America'; has been the name of the continent for just over 400 years.
Because America is not the whole continent. There is also Canada and Mexico.