If you are being plagued by unwanted mail from a particular company, send the offending company a postcard with their mailing label affixed to the back of the postcard. Slash a line through the name and address and write: "DECEASED, please remove from mailing list."
It may take six months to a year to be rid of most unwanted junk mail because some companies use old lists. For us, after a year, almost all mail was being sent to the new man.
Once a company has been notified that you are deceased, they usually remove you from their mailing list - but sometimes they get confused. One man was being pestered by a company that kept sending catalogs to his old name. Finally, he wrote to the mail order company telling them to quit sending catalogs because the man they were writing to was deceased. A few weeks later the company sent a catalog addressed to "Leo Hughes Deceased."