Your "character" in the game is really just whichever ship you happen to be piloting at the time. You can customize your ship's appearance to a certain extent by outfitting it with different weapons, but ultimately this doesn't matter much, since you'll rarely get a close look at other player-flown spacecraft anyway. One of the appealing qualities of massively multiplayer games is being able to have a unique character that looks noticeably different from everyone else, but EVE disappointingly foregoes that opportunity.