Yes. Your mailing address must be current on your DMV files. I recommend that you first change your address online, then apply for a replacement registration.
What do these cookies that you talked about earlier track?
A session cookie may be created automatically on the device you use to access this website, but rest assured that these cookies do not contain any of your personal information and will not compromise your privacy. They are used to store a randomly generated identifier on the device you use to access the site and are erased when you close your browser.