Person I bought laptop from is sharing AVG subscriptions with me without my knowledge

Solution 1:

First, you should use the built in tools to reset Windows completely. You should have done this when you purchased the computer in the first place.

Second, you should not install AVG. AVG is an OK product, but not superior in any way to the built in Windows Defender. If you are using the free AVG product, don't install it.

These steps will remove any connection the previous owner will have had on the computer and as you won't install AVG again there won't be that connection either.