Yes. Previously it was claimed that Paine’s American Crisis III was the source of this name. There are at least two earlier private letters where other individuals use the language “united States of America”, but they use “united” (small “U”) as an adjective. However, on June 29, 1776, writing under the pen name “Republicus”, Paine made the first public declaration calling for the country to be named the “United States of America”, which he already knew would appear on the Declaration of Independence that was soon to be released. Here is an image of Paine’s June 29, 1776 article in the Pennsylvania Evening Post:
