Yup, the correct term is a DEMONYM. Commonly formed by adding -an or -ian to the state name. Here, strangly enough, we are: Ark - Kansan (Arkansan or Arkie for short). Sometimes just -er like New Yorker or sometimes -ite as in Wyomingite or Massachusite (officially, a Bay Stater). From Indiana, officially, a Hoosier.
And don't let Bill con you, he's a New South Welshmen or unofficially Waratahs - Cockroaches - Blues