In the German speaking areas the development of the surnames started in about the 11th century, by the 15th Century, almost all the inhabitants of the German-speaking areas had a last name taken.
For the Herberich name there are currently three theories as to how the name came about:
1) According to the thesis of the name by Hans Bahlow the name Herbrich (and Herberich) is a Middle High German name, which is derived from the German words “camp”, “Night shelters” or “innkeeper”.
2) Another theory is based on a variation of the name Berberich. This name was allegedly given to a family that lived nearby a berberis-hedge.
3) Of the Herberichs from Lengfurt we can almost certainly say that the name is a patronymic, because in 1432 the fishery report of Lengfurt mentions a Kilian Herwig. In later tax lists from the late 15th and the 16th Century the surname is written as Herewig or Herewich. And from about 1650 onwards the name was constantly written as it is known today.
Since not all Herberich families are related to each other, there is most likely no single evolutionary history for the formation of the name.
————————-
Source information:
1) The background image is the first page of the report of the fishermen from Lengfurt, dated 1432, viewable in the Staatsarchiv (state archives) in Wertheim, archival materials G Rep. 44 No. 3.