It all really depends on where your ancestors came from.
If you are a descendant of Christian or Ulrich Shively, then you are Swiss. The name in Switzerland was Schäublin (Schaeublin). When they came to America, it was written the way it sounded: Shively. One descendant who recently visited Switzerland says that the pronunciation of Schaeublin sounds a lot like Shively.
Another variation is Scheible which is the German name. In America, some wrote it as Sheibly and some as Shively.