Kerschen: The Name
The name Kerschen itself has evolved over the centuries. Some Kerschen's changed the name to Kergen and some have changed the name to Kershen. The name Kaerjeng is the modern Luxembourgish word for the sovereign region of Kerschen. Niederkerschen and Oberkerschen are considered the German names for the cities while Bascharage and Hautcharage are considered French names. Prior to the 1900s, every map of Luxembourg I have found used the names Niederkerschen and Oberkerschen. One map in 1594 said "Niederkershen". Bascharage and Hautcharage came into use relatively recently.
Hoheit Kerschen might just be a region where lots of cherries grew. The German word for cherry is "Kirsche" and that could be the source of the name. The French word for cherry is cerise, but the cities are not called Bascerise and Hautcerise, suggesting that the name does not mean cherry. Charage does not have a French translation into English according to the online translators consulted so far. Charage (or charaag) is the Urdu word for lamp or flame, but that seems an unlikely source for the name.
The Croatian word (and name) "Kerschenski" translates as Christian. The Croatian language is also known as Hrvatska. There are also some other Kerschen name derivatives, such as Kerschenmeyer and Kerschenbaum. These families may or may not be directly related to the Kerschens, but Y-chromosome DNA analysis may yet prove a link.
Kerschen might be derived from the much older name "Gershon", one of the three sons of Levi (Genesis 46:11), and it's evolved over the centuries from that [name evolution].
Johann-Baptist Weyrich's historical work on Kerschen history, "Hoheit Kerschen", may shed some light on the issue of Kerschen name origins.