Some people have already gotten confused with Detective Conan and Case Closed. Some have assumed that they are two different types of series only to realize that they are the same. The reason why the name has been changed is the translation of Meitantei Conan to English. If it's translated, it will become case closed.
This can be an apt title to the series because Detective Conan always has the ability to close the cases that he handles. There may be some that will take longer than most but some are just amazing that people immediately get hooked.
Detective Conan was called Case Closed in America due to some issues with copyright when the show transfered to different broadcasting stations.
For this reason, the English version of Detective Conan could not keep the same name and Viz and Funimation decided to call it Case Closed. Everything in the show remained the same as the original except for the show title and the characters were given more Americanized names. The manga has sold over 200 million copies world wide.