We don't. We call it "Sudan".

The United Kingdom, the Ukraine, the Seychelles... it's not just Sudan that has "the" placed before it. The "the" is used for ease of pronunciation.

It's a mistake. For the country, we say "Sudan". For the region (which is not exactly the same as the country), we say "the Sudan". This is short for "the Sudan region". Basically it's a descriptive name, which justifies using "the", but the thing described (region, mountains, desert, islands etc) may be dropped: the Sahara, the Alps, the Carpathians, the Seychelles, the Philippines, and so on. But not always. The United States of America, the United Kingdom, the French Riviera, the Ivory Coast, the Gold Coast, the Czech Republic etc etc keep the full description. In all cases, we mean a specific kind of states, kingdom, republic, coast... As for the Ukraine - well, yes it's for ease of pronunciation. Despite that, the modern convention is to simply say "Ukraine".