Difference of country's name
Recently I am struggling with "the".
What is difference between "Republic of Korea" and "The Republic of Korea"?
I thought it should be either "Republic of Korea" or "the republic"
But it seems "the Republic of Korea" is used a lot.

Question

Answer

Geographical names with the words "Republic", "States" and "Kingdom" are used with "the", it's the rule.

Answer

With 'the' is correct. 
See http://www.grammar-quizzes.com/article4c.html for some rules. That was just the first google match I found.
Notice that we also say 'The United States of America', and 'The United Kingdom of Great Britain and Northern Ireland'.