That's not a thing any American would call themselves. We don't need any "better" name America is ours everyone knows it's us we they talk about America. Saying we should feel somehow guilty about a name is laughable, if you're going to criticize America there are so many more real thing we have done worthy of complaint.
You're sort of missing the point, which is not whether we should want to change the name now or feel "guilty" about it, but whether a better name was available *in the eighteenth century.* (This goes as much for "United States" as for "America." George Stewart's argument that by putting "States" into the very name of the new country, the seeds of nullification and secession were sown, may overrate the importance of words, but it is not frivolous. And note John Calhoun's argument that slavery must be allowed in the territories: "How, then, do we stand in reference to this territorial question--this public domain of ours? Why, Sir, what is it? It is the common property of the States of this Union. They are called “the territories of the United States.” *And what are the “United States” but the States united?* [my emphasis--DT] Sir, these territories are the property of the States united; held jointly for their common use. And is it consistent with justice--is it consistent with equality, that any portion of the partners, outnumbering another portion, shall oust them of this common property of theirs--shall pass any law which shall proscribe the citizens of other portions of the Union from emigrating with their property to the territories of the United States?" http://www.founding.com/founders_library/pageID.2283/default.asp)
Alternate history includes all sorts of things we cannot change *now* (and wouldn't want to if we could) but which might have been done profitably in the past.