In-App Purchases - How can I know who did the charge-back?

You are not privy to customer details from any of Apple's App stores unless you are selling a subscription and the user opts in to sharing data.

Other than requiring the users to make an account to play and working within Apple's UUID / temporary device ID framework, you have no realistic way to determine who is spending money or who is asking Apple for a refund.

Have your lawyer (or you if you're the business person responsible for agreements) look over the terms and conditions that explain when you do and do not get customer data.

Barring that, you can always open a support ticket with developer support since you are a paid developer to ask them to look into any patterns of unusual sales for your specific application. When there is a problem, I've found them to be very helpful in sorting out what's proper and how to adjust things to fit the App Store rules into your business model.