There is no meaningful difference between a world with free will and a fully deterministic world. You're still going to make the same decisions and live the same life in either world.
If you get shot, you die, even with free will.
If you lose your legs, you'll be trapped in a wheelchair, even with free will.
If you get infected by a zombie disease, you'll become a zombie, even with free will.
Free will simply doesn't buy you anything. You can still keep your identity without it.
Without free will you've never made a decision. Try telling anyone they didn't decide what they do or like or wear and you'll see that (for now) identity is tightly tied to free will in most peoples minds.