Now when you "subscribe" to WhizBang online, go to Privacy and create a special credit card just for WhizBang. Give WhizBang a fake name and address as well, and don't use your "regular" email. Create some spares on ProtonMail or some other low-friction service.
When WhizBang goes to verify your credit card, your fake name & address are not checked. You can give them whatever you want.
Your purchase will appear on your regular credit card records. If you want Privacy to use a fake seller, you have to pay for that.
When you want to cancel WhizBang, you just close their credit card. They will get a Decline when they go to charge it, and they'll eventually cancel you. You can go through their official cancellation process, if you want to.
This works. It's what I do.