In Germany, you must register your address at the Bürgeramt. This process is called Anmeldung.
This makes your address as official address in Germany. It's kinda similar to Propiska in Russian, however does not give you any rights for the property, and does not apply any restrictions on the property.
If you're married, bring your translated marriage certificate. It's important!!!!
As a result of the Anmeldung appointment, you get a registration certificate (Meldebescheinigung/Meldebestätigung/Anmeldebestätigung). This document confirms your official address in Germany. You often need it to open a bank account, get a cellphone contract, apply for state benefits, etc.
After your first Anmeldung, you will receive an 11-digit Steuer-ID (tax ID in English) (Steueridentifikationsnummer a.k.a Personnlische Identifikationnummer, a.k.a IdNr). !!Don't mix it up with Steuernummer :) It will come by papermail in 2 weeks, or quicker you can obtain it in person from your local Finanzamt after two days from Anmeldung. Also in the same visit you really should explicitly tell Finanzamt your chosen tax classes, in case you're married.
So, once you moved in your temporary apartment,
- ask landlord for Wohnungsgeberbestätigung(formular is named
Einzugsbestätigung des Wohnungsgebers/Vermieters (Muster)at https://service.berlin.de/dienstleistung/120686/) - book the Anmeldung Termin (aka address registration appointment slot) at webpage linked above.
- In case of unavailable slots, try search it at 8:00h, or use Telegram bot: https://t.me/find_termin_bot