The problem is, FrogNog, that persistent debtors have a nasty habit of pretending to be someone else when debt collectors call, so simply telling them that you're not the person that they're looking for doesn't always convince them. As you suggest, writing to them might help.
I once had a debt collector (looking for someone else) call at my front door. When I told him he'd got the wrong guy he very politely asked if I'd mind showing him some ID, so that he could tell his employers that there was definitely no point sending more debt collectors to my house. When I showed him the house deeds, which showed that I was the SIXTH(!) owner since the debtor had lived here, he seemed convinced!
However I still get debt collectors (and people offering loans) calling my mobile number, trying to get hold of a Debbie England, despite the fact that I've had my number for over a decade. I've even had a call from Ms England's boyfriend, accusing me of stealing her phone and telling me that he was coming round to my house to smash my face in!