In many countries, yes, and it's one of the easiest legal obligations to accidentally violate, because nobody puts it on the arrival checklist next to SIM cards and bank accounts.
Where registration exists, it's rarely optional for visa holders: residence permits, renewals, bank accounts, health insurance, and tax numbers frequently chain off the registration certificate, so skipping it quietly blocks half your admin later and can bring fines or visa complications.
Practical advice: on the day your lease starts, find out the deadline and the responsible office, gather passport, visa, and lease or a landlord letter, and book the appointment immediately, since slots in big cities can run out faster than your deadline.