I think you're over reacting a bit here.
It is a company computer // I technically don't own the computer
Well then what's the problem?
Surely when you go away the person cannot log into your account (if so, ensure you lock your computer when leaving it), so even if they do use your computer for none work related things it'll be tracked on their account (Assuming activity is logged) if not try and get email proof about the conversations just be like when you used my PC did you.... ?.
As long as it doesn't intervene with your work I suggest you just turn a blind eye and just carry on with your job as it really doesn't and shouldn't affect you. If your manager/whomever it concerns does ask you about activity on the computer you have email proof, or even ask colleagues