I have actually given this some brief thought as of late. Nothing in depth, as I don't think they're going to come after a soap maker, but I can understand some concern.
Just so you, and anyone that has purchased my soap, know. I can delete your info at any time. Just email me with the name and shipping address you used, and I will delete it, no questions asked. I have no purpose, or reason to keep it, other than it makes it easier for subsequent orders.
Now, that doesn't mean it's not on a server somewhere. Not technically literate enough to know how that works. But they won't get it from my computer.
There are ways to do things for total anonymity, but it's lengthy, costly, and generally a pain in the ass.