The Stotzer surname may be related or trace back in time to the German surname "STÜTZER" according to the website of Dr. Andreas Stützer. His website is in German. Here's the English translation of his webpage text:
"Der Familienname STÜTZER in Deutschland und Europa (The surname of STUETZER in Germany and Europe):
The name Stützer can be retraced over many centuries. the first references to persons of this or similar name originate from that 12-14th Century. The oldest well-known carrier of the name so far is a Chounrat Stucse, who lived in 1149 in Zurich. In the year 1343 in Bieberach, a Konrad Stuzer is mentioned and in the year 1395 in Rottweil (Germany) a Hans Stotzer. Over the descendants of these persons nothing is well-known.
In the today's way of writing the name shows up for the first time at the beginning of the 16th Century in Switzerland and in Thuringia (Germany): In the year 1515 a Welti Stuetzer in Marignano/Switzerland dies. In Thuringia (Germany) the name appears twice at the beginning of the 16th Century: On the one hand is beheaded a Caspar Stuetzer to 5.8.1519 Vikar of the Johanniskirche in Muehlhausen, on the other hand Ernst Stuetzer to 16.6.1525 in Hoengeda (likewise with Muehlhausen in the course of farmer unrests).
While probably Swiss went out the sex (and thus the name) in the year 1866 in the main trunk, one today still often finds the name Stuetzer in Thuringia and environment. Here the starting point of many supporting he families might be at the same time, because in the passed centuries the main spreading of the name was situated for instance in the area, which is limited in the northwest by Goslar, in the northeast of Magdeburg, in the southwest of iron oh and in the southeast of Jena. From this area meanwhile numerous information is present: "