Good question. I doubt any of them are truly private but I think it at least adds a layer of privacy and security from the service provider, but as with most things it probably won't protect you from a court order.
The only real masked card I can think of would be a gift card paid for in cash. Tedious as it is, that seems like the only way to use a debit card privately, and I think some of those are rejected by online pay platforms.
