I spend a lot of time filing requests to take down my home address. Most low-hanging fruit options have been scrubbed. I am hesitant to increase the count.
Private Mail Boxes are a godsend. In California this can even be the address on your state ID. You do have to give them your residence address but they consider that private information and only share it with authorized agencies.
You mean the link between your name and home address? Impossible to scrub. If you're registered to vote, own a home, or many other things, that is legally a matter of public record.