Kończyce Małe was formerly part of the German Empire. In the German Empire, the place was called Klein Kuntschitz.
The place is now called Kończyce Małe and belongs to Poland.
| Historical place name | Country | Administration | Time |
|---|---|---|---|
| Klein Kuntschitz | Austro-Hungary | Freistadt/Frysztat, Fryštát | before the Treaty of Saint-Germain |
| Kończyce Małe | Austro-Hungary | Freistadt/Frysztat, Fryštát | before the Treaty of Saint-Germain |
| Kończyce Małe | Poland | Cieszyn | after the Treaty of Saint-Germain |
| Klein Kuntschitz | German Empire | Teschen | 1939 |
| Kończyce Małe | Poland | Cieszyn | 1945 |
| Kończyce Małe | Poland | Katowice | 1992 |