If your place doesn't have a toponym in other languages it usually means that it hasn't been very important in history. The people who pushed for this change certainly feel quite the opposite about it, but to me it almost seems self-diminishing. "Our country is so insignificant it doesn't even have a name in languages that don't share our codepage"
Correct, it's not a country but an autonomous region belonging to Finland.
To make things not any easier, the only official language for Åland Islands is Swedish. The Swedish name is just Åland, nothing else. Nobody would call it Ålands öar, well a tourist brochure might call it Ålands örike (empire of islands) but that would sound ridiculous as an official name.
So basically Åland Islands can't be anything but an English name. Maybe not a very clean one because it contains a non-English letter. So Türkiye is not without precedence.
In my experience “Cape Verde” and “The Seyschelles” are more common in English. Martinique, like Costa Rica, is a loan word.
The only recent ISO change I noticed was “the Ukraine” -> “Ukraine” (still heard the old form until a few months ago) and “Belarussia” -> “Belarus”, both 30 years ago.
You would be naïve to think that, especially were you to write that on your résumé. That English has no diacritics is a façade built up to escape the fact that our keyboards make no provision for them.
(A little bit forced, but those are all English words I learned as properly having those appropriate diacritics, when I first learned those words back in grade school.)
Look those words up in the dictionary and they won’t have the diacritics, except as an alternative spelling. They’re loan words, and it’s a stylistic choice.
Ask 95% of laymen to write those words and there will be no diacritics, and the language is defined by its users.
Tell it to the New Yorker, where orthography like coöperate is required by official policy.
As they would no doubt also be happy to explain, the diacritic there is not correctly referred to as an umlaut, as "umlaut" refers to the difference in pronunciation between e.g. German "u" and German "ü", while the diacritic in coöperate doesn't change the pronunciation of any letter but instead exists to indicate to the reader that the two letter Os are to be pronounced separately rather than interpreted as a digraph (as in "troop").
It is somewhat interesting to note that modern English speakers often feel that a mark for this purpose is needed, even though formally the orthography doesn't call for it - but they are much more likely to write "re-emerge" than to write "reëmerge".
It's not difficult to find diacritics in use outside the New Yorker, though generally not in that use. One exception would be the common spelling "naïve".