A demonym or gentilic is the name by which residents of a place are known: New Orleanian, for example, or Norwegian. It is notable that none of the suggested demonyms for residents of Conneticut were recognized by my spell-checker, nor was that given to residents of New Orleans, and nor indeed were the words demonym and gentilic!
It is possibly a controversial field. The Wikipedia article details skirmishes involving residents of Lesbos, the Scottish (as opposed to the Scotch), and many more. Because American is problematic insofar as it isn’t specific beyond a couple of continents, there is some discussion of our options:
United Statian is awkward in English, but it exists in Spanish (estadounidense), French (étatsunien(ne), although americain(e) is preferred), Portuguese (estado-unidense or estadunidense), Italian (statunitense), and also in Interlingua (statounitese).
As happy as I was to learn the words demonym and gentilic, I am happier to now introduce myself to others as a United Statian, which sounds like a breed of dog.