Good and short explanation, but I still have a question: Will the zPIVX I send to someone else show up everytime as PIVX in there history or can I change that?

I know that it is impossible to trace that transaction back to me, but if someone can see that an account gets money out of nowhere it is pretty self explanatory that this account has incomming private transactions and with the amount you are sending an identification should be possible (over invoices for example).