Rájec was formerly part of the German Empire. In the German Empire, the place was called Rajec.
The place is now called Rajec and belongs to Czechoslovakia.
| Historical place name | Country | Administration | Time |
|---|---|---|---|
| Reitz | Austro-Hungary | Reichenau a. d. Knieschna | before the Treaty of Saint-Germain |
| Rajc | Austro-Hungary | Reichenau a. d. Knieschna | before the Treaty of Saint-Germain |
| Rajice | Austro-Hungary | Reichenau a. d. Knieschna | before the Treaty of Saint-Germain |
| Rájec | Czechoslovakia | Rychnov nad Kněžnou | after the Treaty of Saint-Germain |
| Raitz | German Empire | Reichenau an der Knieschna | 1939 |
| Rajec | German Empire | Reichenau an der Knieschna | 1939 |
| Rajec | Czechoslovakia | Rychnov nad Kněžnou | 1945 |
| Rajec | Czechoslovakia | Východní Čechy | 1992 |