That's pretty weird, all right... the only way I can think of that this might have happened is some kind of identity theft, but even that explanation sounds pretty far-fetched.
In any event, I'd recommend sending them a letter telling them that there is no one at your address by the name given on the letter you received and that you know nothing about the debt, all of which is perfectly true. (Don't volunteer any information about your birth name; that's none of their business.) Wait a little while, say two or three months, then check your credit reports to see whether the alleged "bad debt" is listed there, and if it is, dispute it with the credit reporting agencies.
I'm not a lawyer or anything, but a call to your local police department might be a good idea as well. Explain the situation to them and tell them that you're concerned that there may be some kind of criminal activity going on. As it happens, my own name was changed when I was about four years old (due to my mother getting married), and if I got a letter at my home address with that name on it, I'd be pretty worried.