I was charged the wrong tax rate for a purchase. I did move recently. I don’t know how to update it so I am charged the correct (lower) tax rate.
You’re charged the tax rate of your address of record. If you didn’t update your address after moving, Blizzard has no way of knowing.
The only way this might work if you can ask for and receive a refund of your purchase, correct your address, and then re-buy what you bought earlier but with the correct tax jurisdiction.
But refunds are never guaranteed. The standing policy is that digital sales are final; a refund is granted most easily within 14 days after purchase, especially if whatever was purchase wasn’t used or applied.
Beyond those limits, it may be unlikely or even literally impossible to refund, in which case your purchase will stand (as will the tax charged) and you would (and should) correct your address to affect future purchases.
And where is that located?
You can change your personal information including your home address anytime through your Account Details page.
There is an address in your Account Settings, in the Account Details tab.
But without that, the billing address of the payment method would probably be used, I suspect.
This may have to go into a “Purchase Problem” ticket for the Billing team to look at.
https://us.battle.net/support/en/help/product/services/334/1995/solution