There's no right to run an anonymous business. It's illegal in the EU, and a criminal offense California if you accept credit cards. The customer needs to be able to find you and, if necessary, haul you into court to get a refund. You can register a D/B/A name and get a post office box to create a legal identity. That's fine. Hiding behind a web site with "private registration" is a scumbag flag.

Read yesterday's article about how Venmo helps scammers by making anonymous payments easy.