[sneaks on] Chulita as long as the letters are definitely not addressed to you, then contacting the credit checking agencies (there are three you'd need to speak to separately - Experian, Equifax and Callcredit) won't particularly help as they can only edit your details on your request.
Definitely a good idea though to get hold of whichever company is asking you for money and explain that the individual(s) they're looking for have moved on. That company should then update their records and that'll filter through within a month or so to hopefully stop the letters.
It's always worth keeping an eye on your credit rating, but this shouldn't affect it at all. :) If it does appear to have affected your credit report, then by all means stamp your feet and shout at the three credit checking agencies until they fix it for you. As Memphis said, it'd likely just be a simple case of breaking links and/or setting up disassociations.
(Shh - I work for one of the aforementioned credit checking agencies.)