Call the post office. They will typically ask you to put your last name on the inside of your box and then they will tell the carrier to only deliver mail with your name (or ‘Current Resident’ obviously). If you’re lucky, your carrier is nice and respects that immediately. If you’re not lucky, you may have to call the post office every day for a month and complain like I did until they get the point. Eventually that kind of mail stopped.

I’m not sure what they do with all that mail that’s not addressed to me but I don’t really care. The point is I don’t have to see it.

This, along with the other tips in these comments (such as calling customer support lines and requesting removals) means I’m down to literally about one piece of junk mail per month these days.