Rájec was formerly part of the German Empire. In the German Empire, the place was called Rajec.
The place is now called -Rájec (Rájec-Jestřebí-) and belongs to Czechoslovakia.
| Historical place name | Country | Administration | Time |
|---|---|---|---|
| Raitz | Austro-Hungary | Boskowitz | before the Treaty of Saint-Germain |
| Rájec | Austro-Hungary | Boskowitz | before the Treaty of Saint-Germain |
| Rájec | Czechoslovakia | Boskovice | after the Treaty of Saint-Germain |
| Raitz | German Empire | Boskowitz | 1939 |
| Rajec | German Empire | Boskowitz | 1939 |
| Rajec | Czechoslovakia | Boskovice | 1945 |
| -Rájec (Rájec-Jestřebí-) | Czechoslovakia | Jižní Morava | 1992 |