i'm wondering, me and some friends are making a design document for our game, but before i release it i'm wondering will copyright laws protect the name and the story of my game? Another question, what would i categorize my design under? literary works? or what?

You can't copyright names, you can register them as trademarks but that's a different sort of IP.
The story is protected under copyright law though.

http://www.sloperama.com/advice/lesson39.htm