What Major should you study? That depends on the type of Design you want to do.
Systems and mechanics designers would do well to study Mathematics, Physics, Economics, and Programming (I am a Systems and Mechanics Technical designer, and my degrees are in Math and Physics, and I have been a programmer for 35 years).
Narrative Designers should study literature and creative writing. You should also study interactive fiction, if possible.
Level Designers should study art, making sure to learn how to use 3D art packages like 3D Max or Maya.
But, no matter which of these you study, you need to start making games. You won't understand how the above disciplines apply to your chosen craft until you use them to actually build something. It's not a straightforward process, but it's loads of fun.
Best of luck!