Babí was formerly part of the German Empire. In the German Empire, the place was called Trautenbach.
The place is now called Babí (Trutnov-Babí) and belongs to Czech Republic.
| Historical place name | Country | Administration | Time |
|---|---|---|---|
| Trautenbach | Austro-Hungary | Trautenau | before the Treaty of Saint-Germain |
| Babí | Czechoslovakia | Trutnov | after the Treaty of Saint-Germain |
| Trautenbach | Czechoslovakia | Trutnov | after the Treaty of Saint-Germain |
| Trautenbach | German Empire | Trautenau | 1938 |
| Babí | Czechoslovakia | Trutnov | 1945 |
| Babí (Trutnov-Babí) | Czechoslovakia | Trutnov | 1992 |
| Babí (Trutnov-Babí) | Czech Republic | Trutnov | 1993 |