The following online "word list" from the Lakhota language gives
`ce tan< as the word for "hawk" in that language. I suppose it's possible that would be pronounced something like "Chayton" in English, though that doesn't mean it was used as a name in the Sioux culture, or that there aren't other possible or better derivations for it as a modern American given name.
http://www.lakhota.com/online/page3.english.htm#Wildlife