There are different rules for the profile data field and for categories.
The data field should include the place name as the person profiled would have known it, so if the person your are profiling spoke Danish, the place of events in the data field would be Dansk Vestindien during this period.
Categories, on the other hand, follow single language hierarchy streams. Fortunately, specific place names are less likely to exist in more than one language. I think the capital, Charlotte Amalie (https://en.wikipedia.org/wiki/Charlotte_Amalie,_U.S._Virgin_Islands
) doesn't change with the language. So if the person in your profile lived there, I would recommend that you create the category [[Category: Charlotte Amalie]] and nest your profile there. [[Category: Charlotte Amalie]], then could be nested under Category: United States Virgin Islands, which already exists, and also under Category: Danish West Indies, which you might need to create, and nest under Category: Denmark in the English language stream, which already exists. You could also create [[Category: Dansk Vestindien]] and this would be nested under Category: Danmark in the Danish language stream, which already exists.
While in most cases it is tidier to create local place categories with two levels, i.e. [[Category: Cardiff, Wales]], I personally recommend keeping it to one level when possible in a dual language area. Otherwise, you would need to create [[Category: Charlotte Amalie, United States Virgin Islands,]] [[Category: Charlotte Amalie, Danish West Indies]], and [[Category: Charlotte Amalie, Dansk Vestindien]] and nest the one profile under all three, especially if the person was born before 1917 and died after that.
Wikipedia tells me that Charlotte Amalie was once Amalienborg (1691), and before that it was simply Taphus, or "beer hall". Once you figure out the dates these applied, you'll have to deal with them, too if they apply to your profile!