> Will DMV send me a new DL/ID or registration card once my Change of Address is complete?
No. New documents are not issued when you change your address. However, you can request a replacement DL/ID or replacement registration card after you confirm that your address was changed successfully.
If you move, you must notify DMV of your new address within ten days. Submit a change of address online at dmv.ca.gov/addresschange or by mail. It is your responsibility to ensure DMV has your correct mailing address on record.
So, you are required to update your address, and DMV will have your correct address on file, but "you don't have to" update your license.
https://www.dmv.ca.gov/portal/online-change-of-address-coa-s...
> Will DMV send me a new DL/ID or registration card once my Change of Address is complete? No. New documents are not issued when you change your address. However, you can request a replacement DL/ID or replacement registration card after you confirm that your address was changed successfully.