Maybe your first apartment you had a home phone with AT&T as long distance?
Call AT&T, not the collection folks and find out what phone number the bill is about.
You said "My father had recieved his AT&T phone bill with charges on it that were in my name."
Again, call and find out what phone number the bill is about.
Not saying your Dad did, but maybe he used your name to get phone service? There is a reason why they billed him.