According to Wikipedia the name of that village is only “Körkwitz” (without “Dorf”), therefore that’s how it’s in the OSM-Data and how Nominatim expects you to call it. So the question is: Why did you add “Dorf” in your first example?
P.S.: Since your example is in germany: There are more users in the German section of this forum
For Non-Germans: “Dorf” simply means “village”
I still do not understand how Nominatim logic works though. How come Nominatim return “Ostseebad Dierhagen, Darß/Fischland, Landkreis Vorpommern-Rügen, Mecklenburg-Vorpommern, Germany”
There is neither “Dorf” or “Korkwitz” present in the display name.
Surprisingly yes: Nominatim seems to know that “Dorf” means “village” and looks for villages near Körkwitz, and returns them sorted by only Nominatim knows what (since their “priority” is the same; apparently not distance). That’s only a guess, but it would fit to the result