Just because two individuals have the same last name does not mean that they are related. Researchers working on a Smith family know that two people with this common last name are not related, but what about a more unusual surname?
Well it depends on the origination of the name (and that even is not a guarantee) and jumping to conclusions makes for bad research.
One of my ancestral surnames is Habben–a somewhat unusual name. In Ostfriesland, Germany, where many of these families originate the surname is somewhat more common. However, the name is a patronym actually meaning “child of Habbe.” While patronymics was practiced, two men with the first name Habbe would have children with the last name of Habben–though there might have been no relationship.
Sweden is full of Larsons, Carlsons, etc. for exactly the same reason–patronymics.
Even surnames that are not patronymical in origin may be shared by two unrelated individuals. This is especially true with surnames such as Baker, Farmer, Lake and other names that may have been derived from occupations or nearby geographical features.
There may be cases where all individuals with the same surname are related, but let research, not your gut, be your guide. My tentative hypothesis is that all or most individuals with the last name of Trautvetter are related. However, research is not complete and just because the name is concentrated in a certain area of Germany does not mean there was one common ancestor.
Last names can be used as clues to relationships. But a last name only means it was that person’s last name, not that he (or she) had to be related to someone else.