My knowledge is vague. Our family's oral history tradition is that the name is actually "d'Horne" or "d'Orne" (after the Orne River in Normandie, France?). The family arrived in French Canada (in the 1700's?), then headed south into New Hampshire, eventually winding its way to Minnesota, where an ancestor held some type of important political office. According to the history, it was he who shortened the name to "Orne" because it was hard for people to pronounce. My branch of the family made its way into Illinois and Wisconsin. If the story is correct, there is the possibility of family connections in Canada and Louisiana, because the British forced many French onto boats and sent them down the Mississippi. Others fled into New England.