Why "Koran" changed to "Quran"?

Solution 1:

It represents a more careful transliteration:

• There are two different Arabic letters 'ka' and 'qaf' which both correspond more or less to Latin (English) 'k'. They have different sounds, but the difference is not a significant one in English. So an unlearned transliterator might use 'k' for both, but that will lose a distinction in the Arabic, so it is now more usual to use a transcription which distinguishes these two letters, and their sounds, even though people who are unfamiliar with Arabic will probably not make a distinction between them.
• Standard literary Arabic does not have an 'o' vowel, though some varieties of Arabic do. So in the most general Arabic, the word has the 'u' vowel.

Thus in modern transliterations of Arabic, the word will appear as "quran" (or for an even more careful transliteration, "qur'an").

There has been an increasing tendency to replace traditional English versions of foreign words, especially names, by more scholarly or official versions in the last few decades (consider "Beijing" and "Mumbai" as opposed to "Peking" and "Bombay"), though in the end I think this is a political rather than a literary trend.

Solution 2:

The 'K' is the equivalent of Arabic "Kaf" in English and French (mybe other languages), to highlight the difference between 'Kaf' and 'Qaf', using 'Q' instead of 'K' is more appropriate.