Hmm.
That's only part of the basis of Germanic surnames. Another possible influence, especially in the North German language sphere of Scandinavia, is the surname of your father. This is how last names like Johnson, Johanson, Peterson, etc. came about. This especially true for Norwegians, who continued to evolve their respective surnames in this way well into the nineteenth century. This practice was also impressed onto the English language during the Viking invasions of England and the cultural assimilation that followed - so the English language used to use this custom as well. There are millions of people out there with the last name Dickins, which itself is a reference to Dick, the diminutive of Richard; Dickinson is most likely a derivative of that, not a reference to a rather uncultured occupation.
Sources: