Møgelmose was formerly part of the German Empire. In the German Empire, the place was called Mögelmose.
The place is now called Møgelmose and belongs to Denmark.
| Historical place name | Country | Administration | Time |
|---|---|---|---|
| Mögelmose | German Empire | Hadersleben | before the Versailles Treaty |
| Møgelmose | Denmark | Haderslev | after the Versailles Treaty |
| Møgelmose | Denmark | Sønderjylland | 1993 |