Horní Háj was formerly part of the German Empire. In the German Empire, the place was called Ober Haan.
The place is now called - aufgelassen - (Háj u Duchcova) and belongs to Czech Republic.
| Historical place name | Country | Administration | Time |
|---|---|---|---|
| Ober-Haan | Austro-Hungary | Dux | before the Treaty of Saint-Germain |
| Horní Hán | Austro-Hungary | Dux | before the Treaty of Saint-Germain |
| Horní Háj | Czechoslovakia | Duchcov | after the Treaty of Saint-Germain |
| Ober-Haan | Czechoslovakia | Duchcov | after the Treaty of Saint-Germain |
| Ober Haan | German Empire | Dux | 1938 |
| Horní Háj | Czechoslovakia | Duchcov | 1945 |
| - aufgelassen - (Háj u Duchcova) | Czechoslovakia | Teplice | 1992 |
| - aufgelassen - (Háj u Duchcova) | Czech Republic | Teplice | 1993 |