Question

Why do we say "United States of America" instead of "United States" ?

Answer 1

The Declaration of Independence begins:
"In Congress, July 4, 1776.
The unanimous Declaration of the thirteen united States of America..."

Explanation:

The Constitution begins:
"We the People of the United States, in Order to form a more perfect Union, establish Justice, insure domestic Tranquility, provide for the common defence, promote the general Welfare, and secure the Blessings of Liberty to ourselves and our Posterity, do ordain and establish this Constitution for the United States of America."

The form "United States" is a shortened form. The "of America" can be dropped informally because there are no other countries called "United States of...". The other short forms are US (or U.S.), US of A, or even America.

Note: The random capitalization in the quoted texts are as the original documents were written.