Yes, your address may be printed on your residence permit. In any case, you have to register your new address within 14 days after moving at your registration office. You should also inform your local immigration office about the address change by emailing the registration confirmation to them. If required, they will usually get back to you with an appointment for receiving an address sticker for your permit.
π¬ You're reading this in our chat and want to reach out? Simply click on the arrow (<) in the top left corner and select 'I still have a more specific question'.