Kösteldorf was formerly part of the German Empire. In the German Empire, the place was called Kösteldorf.
The place is now called Rájec and belongs to Czech Republic.
| Historical place name | Country | Administration | Time |
|---|---|---|---|
| Kösteldorf | Austro-Hungary | Elbogen | before the Treaty of Saint-Germain |
| Kösteldorf | Czechoslovakia | Loket | after the Treaty of Saint-Germain |
| Kösteldorf | German Empire | Elbogen | 1938 |
| Rájec | Czechoslovakia | Karlovy Vary | 1945 |
| Rájec | Czechoslovakia | Karlovy Vary | 1992 |
| Rájec | Czech Republic | Karlovy Vary | 1993 |