I've seen many different dictionaries and such, and many have a name section where you may put in any kanji. Because I have a Taiwanese origin, I have Chinese characters that can be used as kanji: 王元劭. Are the dictionaries correct and can I choose any reading? These readings don't seem to be kunyomi or onyomi.
Many names in Japanese that are written with kanji can have different readings. That is not to say that they DO have different readings, however.
I used to live in a place called Nogata, but when I was first given the name, I was told I was going to Nakata. The Japanese person who told me had no idea that the reading was different.
However, no one in Nogata would say that the town was Nakata.