That really only exists in English and a few other languages. In German, Polish, Russian and many other languages, there is a different pronunciation for the country of Georgia, while the state of Georgia is always pronounced Georiga.

Georgia the state was named after King George II of England who granted the state it's charter.

The country of Georgia has a much more in-depth and historical explanation.

The Georgia in Caucasus actually has a double duplicate name, since it used to be called Iberia, which is a duplicate with (Spain+Portugal).

There are many duplicate names, not only in America but all over the world. Examples: Paris, Texas; Brooklyn (Breukelen), Harlem (Haarlem). Of course also many varieties with "new" as a predicate (New Jersy, New Amsterdam, New York).

The Netherlands even has duplicates inside it's own borders: http://www.allesopeenrij.nl/article.php?aid=1020

Mind you, we are a speck of a country. France, for example, has many, many more.

Still, I suspect there is a difference between towns in Europe and the names used by settlers in the new world.

So a tag-along question: the naming by the Dutch settlers of for instance Harlem was obviously intentional. Do we know the reasoning behind these choices? What were they?