This sounds like a fun idea, but similar to ehacke I doubt this would be legal. Payment processing is pretty complex and heavily regulated, making this an even harder project.
There are some projects that want to make credit card payments more anonymouse. There are some cryptocurrency credit card providers that have a license to operate, but using cryptocurrencies comes with its very own set of problems.
Another way would be to use privacy.com. They allow you to create multiple credit cards with individual spending limits or ones for single use. So you could have one credit card for your netflix subscription, another one for your Spotify subscription and so one. Unfortunately their service is only available to U.S customers and I couldn't find any alternative for EU customers (if you know of any, please let me know).
I can't try privacy.com myself, but from what I've read an heard, this seems like the most promising option for private credit-card payments.
GNU Taler solves this problem assuming they can find a bank to issue it and merchants to accept it.
At a high level, this is how Google Pay and Apple Pay function now. They create a temporary card number that's used in place of your own to insulate you from being tracked (to some extent).
The primary issue with anything like this is going to be getting VISA and Mastercard to play ball. And if you try to do an end-run around them, they'll just get this whole thing made illegal, if it isn't already.
I think the only way to really make headway in the payment anonymization front is to eventually have something like a cryptocurrency, but without all the speculative garbage that currently comes along with it.