[DragonicRek]

and realize that another person (me) had been using their SN?

Be sure not to associate any Identifiable entity (on your part) with that serial number.

Names, services etc.

If you do get caught, you can always pretend to be innocent and oblivious to what the company is saying
Unless the product is very costly, no charges will be pressed against you

e.g.
"But (sir/mam), that was my friend who posed as me. I would have never done that"
The example isn't the best I admit.
Or you can say, "(sir/mam), I did rent out my house for that time period. It may be that someone se'ed while I was not the owner)
Just something that has the following points
1. It wasn't you
2. You would never do that
3. You have no idea what they're talking about

Or another method is to just never respond to their emails or phone calls
A company wouldn't be able to afford too much resources for just a measly <200$ product