The Portuguese were one of the first countries to trade extensively with Japan. They were also the first (1603) to attempt to represent the Japanese language using the latin alphabet (the English alphabet).
This first translation of "Nippon (日本)" was "Jippon". Many European languages adopted various mispronunciations of "Jippon". In French, it became Japon. In English, it became Japan.
So the word Japan is a mistranslation of a mistranslation of "Nippon". At least it's closer than the name Marco Polo gave Japan ~ Cipangu (15th century).