Well... when it comes to a place name, what is the definition of "correct pronunciation"?
If you live in a small town whose inhabitants all speak the same language and that has not been discovered by international tourism, then the answer is simple - the correct pronunciation is whatever pronunciation is used by the town's inhabitants.
But how about national capitals and major tourist destinations that are called different things in different languages? Is it Warszawa, Warsaw, Warschau or Varsovie? Is it Munich or München? Is Berlin "bur-lin" or "bair-leen"?
As for Copenhagen... here in England we say "Copen-haygen", and that's also how my Scandinavian friends pronounce it when they speak English. But I don't think there is any right or wrong pronunciation in English because it's just an English rendition of a Danish name. And the Danish pronunciation is quite different!