Since Nina is derived from names like Antonina, it is usually pronouned as Neena. Also, this is how the letter "I" is pronounced in most languages. Maybe it is only in English that "I" is sometimes pronounced the other way.
"You may give them your love but not your thoughts. For they have their own thoughts. You may house their bodies but not their souls, For their souls dwell in the house of tomorrow, which you cannot visit, not even in your dreams." (On Children by Kahlil Gibran)