demonym

demonym – a demonym or gentilic is a word that denotes the members of a people or the inhabitants of a place; in English, a demonym is often the same as the name of the people's native language: e.g., the "French" (people from France)

"And if there's one thing that the candidates want to show they really know about Indiana, it's the local demonym..." (i.e. Hoosier.)

--Heard on NPR, in this story.

Words that describe the inhabitants of a place. See this list for a bunch of examples.