REIDINGER as a surname would be someone from Reiding or Reidingen. But I can't find either of these place-names on a German road map; maybe it does not exsist any more. The name may have somethinmg to do with "Ried" (reed).
DORNHAGEN is as easy to explain as it is hard to find. "Hag" means "bush, little forrest" or "a piece of land surrounded by bushes". But what my road map didn't know - map 24 found it: Dörnhagen (with an O umlaut, which can easily be dropped abroad), a small community south or Kassel (central Germany).
So to check place-names, go to http://www.de.map24.com/