Has anyone tried this?
You cannot. As well as PayPal cash/debit, and similar services offered by cashapp & chime.
Privacy.com cards are for blocking companies from charging you money you don’t want spent. It is not for obfuscating your actual identity.
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”