Remember: Visa/MC cannot verify cardholder name. They pretend that they can and merchants believe that they can but there is no mechanism to do so.[1] If the numbers match up, you can use "Mickey Mouse".
No online retailer/merchant/provider has ever seen our real name (or real address). We created a pseudonym and attached it to a PO BOX in our town and a twilio phone number.
This doesn't solve every problem but it does solve the simple issues of identity theft and impersonation or (very low level) attackers correlating our activity to other activities.
YMMV. IANAL.
[1] There is some weird "verified by visa" thing that does attempt to confirm identity but I've only seen it once in the last 12 years ...