I'd be inclined to take photocopies of each letter as it arrives, and bring the original down to the local police station. If you explain that you've got a series of letters and fear that someone's using your address to build up a false identity, they'll tell you who to contact in the police department.
It could be some sinister scammer; on the other hand, it could also be an idiot student. Friends of mine in my youth, a bunch of drunken students, got a series of letters about library fines years later addressed to a name they did not recognise - until they realised that they'd registered the household cat for a library ticket. It could be something like this - but better safe than sorry.