The answer to the first question might be easier than the second. According to the History Channel’s This Day in History, Sept 9th 1776, Congress officially renamed the new country the United States of American, replacing the traditional United Colonies.
One of the aspects of this that I find interesting is that it took almost two months since the signing of the Declaration for this name change to happen. By day, I am a marketing consultant. I understand how crucial branding is to the success of any new endeavor. Heck, we would have had t-shirts made before the ink even dried on the parchment.