there are 3 Möderndorf, 2 in Carinthia, 1 in Upper-Austria!http://de.wikipedia.org/wiki/M%C3%B6derndorf
Oswald von Möderndorf (name after the place!)is attested in documents since 1375, in 1458 we hear of a Siegmund Weidegger, all vassals of the Count Palatine of Gorizia.
Through the Peace of 1460 Pusarnitz this Gorizia possessions fell to the Emperor Frederick III. The Habsburgs Möderndorf awarded to the counts Slamanca-Ortenbourg. In the 17th Century came the Lords of Rechbach, the Wiedmann and finally bought Prince Johann Ferdinand Porcia 8 October 1662 Möderndorf. Thus, the country jurisdiction came into the castle. From about the middle of last century, the Waldner family owns. From them is acquired KR Georg Essl. he completed the building of the club promotion Gail Valley Heritage Museum for the establishment and management of a museum are available. http://www.kultur.kaernten.at/?arid=9830&jid=SO&siid...
and i guess more that your Möderndorfer are named after a place Möderndorf, the question then would be - WHICH ONE.
Möderndorfer -> a person who comes from Möderndorf.