This question has been discussed in various fora more than it probably even deserved, may the gods of linguistics forgive me for contributing to that.
Quite simply the Anglophone world had no direct contact with what is now Ukraine, nor was English a lingua franca in Eastern Europe in that era, at the time that some cognate of Ukraine entered the English language. So toponyms, ethnonyms and so on in English tended to be inspired by French, German or even Latin in that era.
From the few historic mentions of Ukraine in English, we can try to infer whether it was more French-inspired or Latin-inspired or even perhaps Polish-inspired:
1651 Ukrain, 1671 Ukraine, 1688 Ucrania, Ukrania, 1762 Ocraine.
Slavic languages typically have no definite or indefinite articles, whereas French and German uses articles with many more countries and regions than English do. Both French and German still use the definite article with Ukraine -- l'Ukraine and die Ukraine -- as French also does for France and many other countries, and German does for Switzerland and some other countries.
This is also true for regions or countries in or near Ukraine: die Moldau usually, die Bukovina or das Buchenland, das Banat, das Kosovo or der Kosovo, die Batschka, die Krim, die Dobrudscha, die Slowakei and, again somewhat controversially, die Tschechei, but Moldawien, Galizien, Ruthenien, Bessarabien, Siebenbürgen, Tschechien.
There is a logic to this in the sense that based on lexical features a native speaker would impute an article and gender for a name he or she had not heard before, but there is no geopolitical logic to it in the sense that article or lack of article does not imply a greater degree of autonomy or official status.
That said, French uses en Ukraine, that is, there is no definite article when saying in Ukraine. This is not specific to Ukraine but to the preposition en, it is the same for la France itself, and for most if not all other countries or regions which take a definite article.
In English, there are fewer geographical regions or countries with the definite article, and we can say that there is likewise no geopolitical meaning to it. The common name of a certain global superpower has an article, as do the United Kingdom, the Russian Federation, the People's Republic of China and so on.
So there is no fundamental linguistic basis for this drama, in the sense that there is no definite article in Slavic, and no geopolitical meaning to the definite article in the relevant European languages that do use definite articles.
As a political and personal matter, most of us try to respect the wishes of countries, cities, organisations, persons and so on with regard to their own official name for themselves in various languages. See the cases of Ivory Coast, Burma, Macedonia, South Korea, Czechia, Constantinople, Calcutta, Bangalore, Golda Meir, Cat Stevens and so on, to say nothing of the maiden name concept. And likewise most of us are a bit forgiving if other persons do not instantly or consistently update their names for all such entities and persons in all contexts in all languages. That is outside the scope of this SE.