Leingang is also the short-form of the German ”Alleingang ”
(it means : man who goes alone = allein):
This could be a possible explanation for the origin of the Name Leingang:
Perhaps, the first Leingangs had been people, which – for whatever reason - had been known as loners.
Alternatively, people who did not want to have contact with others, perhaps that didn’t want to ask for help from other people, but always tried on their own. In German: im Alleingang, in English: single-handedly or independent.
Perhaps this Alleingang in the German language changed to Leingang through the times.
Today, when anybody asks me for my name, and I say Leingang, and are asked for the correct spelling of the Name, I say: like ”Alleingang” but without the Letter A.
This is not quite correct, but everybody can write Leingang after that.
In my opinion, there is not much to say against this version.