Will U.S brokers accept a utility bill as a proof of residency-address (when opening account) if it is registered in my father's name?
Ultimately, only your broker can answer this question. I would ask them directly.
Most proof-of-residence documents require both the address and your name. If your name is not on the utility bill then they probably won't accept it. Your best bet is to provide a government ID, some sort of school enrollment document (if you are a minor or at college), or a pay-stub. Again, it has to include both your address and your name.