In Germany, you must register your address at the Bürgeramt. This will become your official address in Germany. This is called the Anmeldung.
During the Anmeldung appointment, you get a registration certificate (Anmeldebestätigung). This document confirms your official address in Germany. You often need it to open a bank account or get a cellphone contract. After your first Anmeldung, you will also get a tax ID (Steueridentifikationsnummer).