For English it's true that calling it "the Ukraine" feels like you're talking about a region instead of a country, because that's the (historical) reason for the article. So in English "the" does have that implication.
In German however, we use the article for very different, purely grammatical reasons: Every noun in German has one of three gramatical genders, that have nothing to do with its physical nature. A pouch isn't more male than a bag, but nonetheless, we say "der Beutel" and "die Tüte". The same applies to country names. Some are male (der Iran), some are neutral (das Syrien) and some are female (die Türkei). And for countries that are neutral, you just leave out the article in almost every case^1^. It has nothing to do with wether something is a region or an independent country.
A good illustration of this: In German the same country can sometimes be refered to in two different ways with two different genders. "Die USA^2^" is female*, "Das Amerika" is neutral. So you would say "ich fahre nach Amerika" but "ich fahre in die USA". Or an even more obvious case: The Netherlands are often called "Holland" in German, even though Holland is just one region in the Netherlands. But Holland is neutral and Niederlande female. So we say "ich fahre nach Holland" but "ich fahre in die Niederlande". Here the country has the article, while the region does not.
^1^ In some cases the neutral article shows again. For example, if you're talking about a specific version of a country: "Das Frankreich der 50er-Jahre" or "Das Spanien unter Franco"
^2^ The USA are female because they are plural, and every plural is female in German – "Der Mann" but "die Männer" – showing that gramatical gender has no physical reasoning.