well many countries do have 2 names isn't it?
But the definition of UK, Great Britain or England is wrong
UK = United Kingdom
United Kingdom: England, Scotland, Wales and Northern Ireland
Great Britain: England, Scotland and Wales
England: England only
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Some nations have two names because one is from their native language and second name coming out from other nations ... the way they feel easy to call other nation. For example when Pakistanis are talking about India they use the word "Bharat" but indians prefer to use "Hindustan / India" or English prefer to use "India".
May be language differences? or historical they were known with these names and now all names have become common for them