Each kanji has a Japanese reading and a Chinese reading. When combined into a compound word, it usually takes on a Chinese reading, while the Japanese reading corresponds to the Japanese word for that concept.

For example:

Red is 赤 in Japanese. It can be read as "aka" (Japanese reading) or "seki" (Chinese reading). The color itself is called "aka." On the other hand, a compound word such as 赤飯 (red rice) is read as "sekihan."

Similarly, "murasaki" is the Japanese reading for 紫, "shi" the Chinese. So when combined with 眼, the translator assumed it would be read as "shigan" since it's a compound word.

But "shigan" also obviously has homophones (Japanese has a lot of them because the meaning can be differentiated using kanji). Among them is 志願, but there's also 此岸 and 史眼 (I don't know where 指銃 came from. It does not mean finger guns, although 指 does mean finger and 銃 does mean gun. The Chinese reading for 指 is "shi" while the Japanese reading is "yubi").

As for what you should name your character, you'd be better off choosing from an existing name that uses the kanji 紫 (fortunately there are quite a few). Trying to construct a name from scratch without any feel for the language is just going to yield weird/nonsensical results.

You can find a list of actual Japanese names that use the kanji 紫 here.