I usually don’t.

Unless its a food delivery, then I just try to find a white male name, to avoid racial profiling/harassment.

I dont think that really do much in terms of privacy, the merchant is gonna know who you are. And sometimes they will reject an order if the name used in the order doesn’t match the name of the card holder.

Any card/bank transaction, anything that gets sent to your address, that’s not really something you can have privacy over. Unless you use cash payments and use someone else’s address. Its very difficult to hide financial activity.