None of the founding documents ever were written “the united states of America” so Anna is correct.
Neither The Declaration of Independence nor the Articles of Confederation capitalized united in their headings., both were “united States”.
However Article I of Articles of Confederation: The stile of this confederacy shall be “The United States of America”.
Here is an example of Anna contradicting herself. She claims the name “The United States of America” is the name of a corporation while the name “the United States of America” is not. That might be true in the modern definition, but does not appear to be so in 1778.