From a legal perspective, your contract needs to have the address you rented. It’s the same as if you bought or leased a car, it can’t say you bought car A with vin #1 when you bought Car B vin #2.
I was visa-exempt, got a residence certificate at immigration and walked into K-bank walking out 30 minutes later with an accout. If course I need my passport and a 2nd ID, but it couldn't have been easier