Rýnek was formerly part of the German Empire. In the German Empire, the place was called Rienek.
The place is now called NN and belongs to Czech Republic.
| Historical place name | Country | Administration | Time |
|---|---|---|---|
| Rienek | Austro-Hungary | Senftenberg | before the Treaty of Saint-Germain |
| Rýnek | Czechoslovakia | Žamberk | after the Treaty of Saint-Germain |
| Rienek | Czechoslovakia | Žamberk | after the Treaty of Saint-Germain |
| Rienek | German Empire | Grulich | 1938 |
| Rýnek | Czechoslovakia | Žamberk | 1945 |
| NN | Czechoslovakia | Rychnov nad Kněžnou | 1992 |
| NN | Czech Republic | Rychnov nad Kněžnou | 1993 |