As was stated, do not use your name, use any made up name you want, this will avoid any and all bill collection problems.
If you get a bill, writing cancel on it and returning should clear up the majority of problems
If you receive a letter from a collecion agency do not automatically flip out. Yes there is a chance it could land on your credit rating (which would be VERY bad), but oftentimes companies merely just send a list of delinquent subscribers to an agency and they send out form letters. You can write a polite, but firm response to this agency insisting you have never signed up for said magazine, you have no desire for said magazine and whatever bills they have previously sent either never arrived to you or you have expressed a desire to cancel an incorrect subscription.
You cold also roll the dice and do nothing, and maybe it will all go away, but write the letter to set your mind at ease and explain either it was supposed to be free, or you have not signed up for any magazine, nor have your recieved any magazine or desire as such.