As used (or not) in the names of countries.
One does still occasionally hear or see the Ukraine, but be careful not to use that around people of Ukrainian origin. They can get very shirty about it.
Their point is that the definite article the makes the country sound more like a region, like the Midwest or the Highlands – and, by implication, a sub-division of some larger entity.
And we all know which larger entity most Ukrainians are not longing to be part of again…
This is all fair enough, geopolitically speaking, but perhaps not linguistically.
First, Ukrainian (like other Slavic languages) uses no articles at all (no a, an or the), so perhaps can’t really dictate when English uses them.
Secondly, there are countries that do take an article as part of their names.
The definite article is part of the official names of The Gambia and The Bahamas.
The definite article is often – even usually – used with a range of other nations, as a matter of idiom. Many are archipelagos or include a form of government as part of the name, but not all: Central African Republic, Channel Islands, Comoros, Congo, Czech Republic, Dominican Republic, Lebanon (especially for those who know their Human League back catalogue), Maldives, Marshall Islands, Netherlands, Philippines, Seychelles, Solomon Islands, Sudan, United Kingdom, United States of America, Yemen.
(The) Congo and The Gambia each takes its name from the river that runs through it.
But, if you’re likely to be read or heard by Ukrainians, the country is just Ukraine.
The Dominican is also likely to irritate Dominicans, for whom it is always the Dominican Republic (or sometimes even the historical Santo Domingo).