The title says most iconic but the poll says greatest? Greatest is very debatable, but I'd say Poe and Fitzgerald might be most iconic. They're so widely known-- who hasn't read Gatsby in high school?
Twain undoubtedly. Also had arguably the greatest international reputation as an "American" writer. He's slept on because most curriculum only requires reading of Huck Finn. After that for me is Hemingway because he's kinda the writer's writer, I believe he won some poll a few years ago amongst American authors. After that it gets murky, but those two are the premiere, in my opinion.