Gaj was formerly part of the German Empire. In the German Empire, the place was called Hain.
The place is now called Gaj and belongs to Poland.
| Historical place name | Country | Administration | Time |
|---|---|---|---|
| Gay b. Blociszewo | German Empire | Schrimm | before the Versailles Treaty |
| Gaj | Poland | Śrem | after the Versailles Treaty |
| Hain | German Empire | Schrimm | 1939 |
| Gaj p. Błociszewem | Poland | Śrem | 1945 |
| Gaj | Poland | Poznań | 1992 |