You can't with privacy.com or other big services, but there are other services that let you either generate a no-KYC reloadable credit card, or buy a prepaid international card that works for almost everything.
In my experience, it does a good job of obscuring my identity from websites with questionable security practices (e.g. ones that rolled their own payment processors and are clearly questionably coded, or just ones that could be).
And it obscures the nature of your purchases from your bank.
Update: especially because, recently, some banks will use your transaction history to advertise to you, I feel even better jumping onto one with stricter rules regarding that
You can use a Privacy card with any name you want on it although some small vendors with actual people running the purchase process can read and take issue when the "card" is supposedly issued to a "Mybig Blackdog"
Yes... the entity you are spending money with will not know your name (unless they need to due to transaction issues etc.)...but the transaction units entirety is recorded with your name and the business the money was sent to.