Yes.
They call themselves the Diné. :)
They call themselves Rastas.
they call themselves tamalians
you go walking around with velcro and if someone sticks to it, they are the black separtists.
They called themselves catrachos and argentinian cal themselves argentinians
They call themselves Evangelicals
They call themselves Muskogee, or Muscogulge
No. They call themselves Muslim, but not Arabs.
Germans call themselves "Deutsche" in their native language.
Anyone can call themselves pastor, but that doesn't make them one.
Switzerland is the home to those who call themselves Swiss. Japan is the home to those who call themselves Japanese. Canada is the home to those who call themselves Canadian. Perhaps this is an incomplete question?