Rzasnia was formerly part of the German Empire. In the German Empire, the place was called Ronsau.
The place is now called Rząśnia and belongs to Poland.
| Historical place name | Country | Administration | Time |
|---|---|---|---|
| Rzasnia | Russian Empire | Novoradomsk | 1914 |
| Rząśnia | Poland | Radomsko | 1921 |
| Rząśnia | German Empire | Welungen | 1939 |
| Ransau | German Empire | Welungen | 1939 |
| Ronsau | German Empire | Welungen | 1939 |
| Rząśnia | Poland | Pajęczno | 1945 |
| Rząśnia | Poland | Piotrków | 1992 |