Can I say "Behind story" instead? Also, without the preposition "about" still makes sense?
No, you cannot say "behind story" here, because this is not grammatically correct, since it would change "behind" to an adjective instead of a preposition. "Story behind" is used to refer to a story about something, and the word "behind" is used as a preposition. You can replace "behind" with "about" and it would still make sense, although "behind" is more commonly used in this case.