Gaj was formerly part of the German Empire. In the German Empire, the place was called Gay.
The place is now called Gaj and belongs to Poland.
| Historical place name | Country | Administration | Time |
|---|---|---|---|
| Gay | German Empire | Strelno | before the Versailles Treaty |
| Gaj | Poland | Mogilno | after the Versailles Treaty |
| Gay | German Empire | Mogilno | 1939 |
| Gaj | Poland | Mogilno | 1945 |
| Gaj | Poland | Bydgoszcz | 1992 |