What is the ruling on opening a phone line in another person's name with their knowledge, then that person failing to pay the installments due to the state, despite not using the line, and does sin befall the person whose name is on the line?

You must fulfill the contract with the institution and pay what is due on it because you are the contracting party and your name was written. Allah Almighty commanded the fulfillment of contracts: (O YOU WHO HAVE BELIEVED, FULFILL [ALL] CONTRACTS). If you enabled the other person to benefit on condition that he pays the installments, then you can demand them from him.