You are probably looking for a different Acorn line. The Acorn's were actually descended from Germans who were mercinaries for the British during the American Revolution. They were called Hessians, and actually had the name Eichorn. After the war they were afraid that the Americans would hate them so they moved to Canada, mostly Prince Edward Island, and changed their name to the more English sounding, Acorn.
If you are looking for Native American Acorn's, most likely they named themselves after a tree. Indians usually took names of nature things, ie. Red Cloud, Crazy Horse, etc.