Gaj was formerly part of the German Empire. In the German Empire, the place was called Hein.
The place is now called Gaj and belongs to Poland.
| Historical place name | Country | Administration | Time |
|---|---|---|---|
| Gay | German Empire | Löbau | before the Versailles Treaty |
| Gaj | Poland | Lubawa | after the Versailles Treaty |
| Hein | German Empire | Neumark (Westpr.) | 1939 |
| Gaj | Poland | Nowe Miasto Lubawskie | 1945 |
| Gaj | Poland | Toruń | 1992 |