Good morning, Budrys.
(1) I do not think there is a "rule."
(2) It's just what native speakers decide.
(3) When I was younger, we always referred to THE Sudan. Today almost all Americans say only Sudan.
(4) When I was younger, we always referred to THE Ukraine. But not nowadays.
(5) I have noticed that other languages are also dropping "the" sometimes.
(a) Until 20 (???) years ago, Spanish-speaking people always referred to THE United States. I notice that most Spanish-language publications no longer use "los" (THE).
P. S. I forget to mention that we used to refer to THE Lebanon. It would sound very strange today if an American used the article.
Have a nice day!