Earlier quoted context omitted.
They probably mean endonymy and exonymy. https://en.wikipedia.org/wiki/Endonym_and_exonym Different groups can have different names for the same thing. For example, country names change depending on the language.
So "both" means a) the endonym and b) the exonym of the country in which the user is currently located? Makes sense, I guess. Edit: However, as far as I can tell, there IS no endonym in this case, so it should be exonyms all round?
So yes, there are only exonyms.