Honestly, I don't think Americans are any dumber than any other nationality. The difference is we put them on the TV as a form of entertainment. Look at the media, we watch sitcoms about characters who are dumber than the bagel I am eating... so long as the bagel were sentient.
I'm an American myself, screen name aside. I understand the whole "there are other Americans" idea. When my brother told his wife's uncle (she's Italian) I was from America, he asked if I was from Brazil. I was 14 at the time (1999), and it did not phase me in the slightest. My home state (Wisconsin) is middle range in size and population in the USA.
I do get offended and perturbed by the generalization "Americans are stupid" nonsense. My brother has lived in Europe for nearly twenty years now (he is 15 years older than me) working as a scientist, and he laughs at the concept. He has the same opinion I do, that Americans are no more and no less stupid than Europeans certainly. It's harder to gauge compared to other regions of the world as most of the people he knows from Africa, Asia, South America, and Australia all have doctorates or at least a masters in a scientific field... but I suspect the same trend would be found.
One also has to remember the USA has over 300 million people, compared to other nation-states that is rather large. Only India and China have larger populations. So it stands to reason we'd have more idiots simply by having more people. Wisconsin (again mid range in population) has more people than Finland.
You have to understand how dumb some Europeans seem, despite their actually being intelligent, when they refer to me as a Yankee. I'm from the midwestern United States. I'm not a "Yankee". A Yankee is from New England. Now, I'm not offended, more amused. Now if you call a southerner a Yankee it'd be like calling a Scotsman an Englishman or a Slovakian a Czech (or vice versa).
I've been asked by Europeans who were going to visit New York City how much time they would need to set aside to go see the Grand Canyon and I asked "Are you flying or driving?" They looked at me oddly and said, "Well driving of course". I told them "Set aside over a week", and they were astonished. They didn't realize how truly large this country is. When I go from Wisconsin to North Carolina to see my sister, my family makes a trip equal in length as a drive from Paris to Warsaw. Wisconsin is even larger than England (not the UK mind you). When we went to see my (late) Grandfather, we made a drive equivalent to driving from Paris to Moscow!
Due to our size there is slight differences in culture. The Pacific Northwest, the Midwest, the South, New England, and the West Coast are noticeably different in culture. Not as profound as going from France to Germany I grant you, but still you notice it when you grew up here. To understand the people of the USA, you need to understand how truly large our country is and how spread out we are. Also you have to go to the midsize cities. Not the metropolises of New York or Chicago, nor the small towns either.
Granted, I have a degree in history and political science so I probably have a better understanding of the world and its cultures compared to the average human on this planet (as does anyone who studies these subjects heavily and I suspect some of you fit this bill too), and I have gone overseas several times. Still, I wouldn't say America as a whole is any more ignorant than any other culture. I've spent time in foreign metropolises and in the rural areas as well. The main things that change are the smell of the food, and the languages. I've met strikingly ignorant Frenchmen, incredibly rude Italians, shockingly bigoted Brazilians, etc that are worse than any stereotype of Americans.
Overall I think we, like most cultures, worry about our own ignorance so we focus so much of our media on the morons in our society as a form of entertainment. Their stupidity is truly hilarious, but it also reassures us that we are not as dumb as people would like to believe.
Edit: On the original topic, we don't have a better name. We really don't. As said "Yankee" certainly doesn't work, as it is a region of our country, really.