It‘s as private as the process of buying a gift card can be:

Online at e.g. g2a.com, offgamers.com or kinguin.net you obviously need to be a bit careful with your identity and identity connected payment options.

You can always buy a virtual credit card via TheBitcoinCompany app and then use this as a payment in these online-shops.

In stores e.g. in Brazil, Colombia or Costa Rica there is no problem. Just buy one and redeem it online. No need for verification.