This is a specific question that may result in a more general answer. I have an ancestor who was born in the Schleswig region during the dispute between Prussia and Denmark. The region had both a German name and a Danish name and there were many disputes over which name to use - the Schleswig-Holstein Question remained outstanding from 1848 to 1864, and truly wasn't resolved until the end of WWI in 1918. My ancestor reported his country of birth as either Germany or Denmark in US Census records depending on the state of the war at the time, and the reason he left was due to not wanting to be drafted into the Prussian/German military. By the time of his death his home town was firmly in Denmark, and he identified with the Danish region (despite the very German-looking last name).
For now, I have his birth location as Tønder, Denmark, but I don't think that's right no matter what I choose. It's currently in Denmark, which should be Danmark if I use that. It also seems like it could be Hertugdømmet Slesvig, Herzogtum Schleswig, Schleswig-Holstein, or even Sønderjylland. Of those, only Danmark currently has a category, but that just means one hasn't been made for Duchy of Schleswig yet.