As of 1828, in Germany, there were already Kuhns, Kiehns, Kuehns, and the whole mix, as evinced by the Rank and Quarterlist of the Prussian Army.
My family is Kean, and has been since we got off the boat in 1828.
The best explanations I have ever heard are, Kuehns are illiterate sheep farmers and migrants who do not know how to read and write.For my family, this does not hold water, because my immigrant ancestors could not only read and write, but could read and write math.
The second best explanation is, Sometimes, blacksheep nobles, war heroes and fugitives take on a false name--for instance, Der Krohn (The Crane.)
In any event, the names have been different since at least 1828, and probably long before.