You can never have a complete blank slate character in a video game, because some things are always going to be defined for you. You'll be limited to available classes and races. You'll be limited to characters who want to accomplish whatever needs to be accomplished, in the ways you're presented of accomplishing it. As the game goes on, you may need to adjust your character concept in order to continue - if you're playing a hardcore pacifist, for example, and you come to a point where you must kill someone in order to advance, you'll either need to adjust your character or quit and make another one. Or headcanon the heck out of the situation and write fanfic afterwards. That tends to be my strategy.
Everyone has different ideas about just how many restrictions they're willing to accept. There are some games I refuse to play because I can't customize the main character enough, but, on the other hand, if I have to deploy headcanon a lot because the game can't react to the elaborate imaginary backstory I was given the freedom to make up, I end up disconnected from the world and the story.
I'm glad I'm not a game developer because I have no idea how to strike a good balance between those extremes.
