Trollinger is a variation of Drollinger, which itself may have originated as "Tyrolinger," Drollinger may have been the first written variation but was widely used by the 3rd known generation of the family name.
Drollinger is of German origin and means people from Tyrol. In old German especially it is pronounced with a T, and therefore was often changed to Trollinger when migrating. Historic Tyrol is a geographical area of the Alps that today is in Italy and Austria, therefore Drollingers were a class of people rather than a family, per se, and may not have been directly related before migrating. Today the name is most associated with the Baden-Württemberg area of Germany, although the name is widespread in the United States.