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Did you ever give comcast another address after you moved out? I was in a similar situation about 4 years ago after I moved out of my first apartment.
Moved into my first apartment and had my first cable and internet service there. First one ever in my own name. About a year later the apartment next door to me burned down and thus I had to move out of mine as well. I moved back in with my parents for the time being while I search for a new apartment. So when I went to the comcast office to cancel my service at my old address they asked me for a new and current address that they could send the final bill to. Seemed fair enough so I gave them my parents address.
Well a month later i get my final bill, in addition to the bill for someone else I didn't know at an address I didn't know. Someone elses service had been attached to my name.
I ran down to the comcast office and after pleading with them that I have no clue who this other person was on my bill they took it off. Glad I took care of it quick before it became a serious issue.
Only one of two things could have happened. Gross incompetence and the comcast rep "accidentally" added someone else's service to my bill when they should have cancelled and sent me the final bill instead, or straight up fraud and the comcast rep tried to get someone free service at my expense. Neither of which I like and just upsets me.
You have to sign for stuff like this. Give them hell OP. Ask them to provide proof that you yourself authorized that service at that address. If they can't come up with it give them hell.