None of that is of any concern to PayPal. PayPal's only concern is that they paid back your customer, so now they have to get their money back from you.
I haven't given my correct identity in my alternate paypal account.
Now you're talking about fraud. In fact, I don't know what country you're in, but you are probably dangerously close to (if not over) a dangerous legal line. Using false information to open a bank account can have some serious legal repercussions.
I'd say a chargeback is the least of your worries at this point.