This history comes mostly from my two cousins Sharon Kay Stoll, and Denise Stoll  McCoy. Sharon did some research while in Europe in graduate school. Here are some  excerpts.
    The Stoll family originated from Switzerland. The family lived in Messen,  Buchenberg, Switzerland. The father Bendicht, was asassinated in Larochenett,  Switzerland, where he lived. One of the murderers' name was Frossart (the Stoll  family history spells it Fropart. This is wrong.Two ss's are mistaken for two p's) of  Montanchy. He,Frossart,was executed in Parentry. The other was a Frenchman of  Lorraine and being of Catholic priestly family, he escaped the wrath of the law.    The Stolls must have emigrated with the Grabers from Switzerland to France when  the persecution by the Zwinglians got to be too much. The Stolls lived around  Couthenans, France, after leaving Switzerland. They were Mennonites. The Stolls fled  to America in the mid 1800's when persecution by the Catholic French became too  great.  
    I am adding information on Grabers from my cousin Sharon Stoll. It is very  confusing. Generation after generation they named their children the same thing and  then married cousins generation after generation. I am trying to merge duplicates. I  may have fifteen Catherine Grabers with no birth or death information. Some of them  are duplicates but I can't tell. Every Peter Graber married a woman named Catherine  Graber who was his cousin.  I will also be adding information from the Wayne county  genealogical library on Kaser and Shondel.

Stoll Name Meaning and History
 German: from Middle High German, Middle Low German stolle ‘prop’, ‘support’, ‘frame’,  hence a metonymic occupational name for a carpenter, or a nickname for a rigid  person. 
 Jewish (Ashkenazic): unexplained.