You need to use a non zap enabled lightning address to stay private.
Discussion
For now
Of course i can send people tips off nostr and nostr wont know about it, but thats a worse UI. I want private zaps option.
I think you misunderstood me. If you have a non zap enabled lightning address in your bio you can be easily tipped but you won't she where its coming from. However the ones who tip you can she it from their client it their client support zaps.
I believe there is work in progress on anon zaps.