Unfortunately, Anthropic doesn't seem to offer a mode where it doesn't know who you are, except for its crippled "Incognito" web UI.
Ultimately anonymity from AI that you're talking to will be a losing battle, due to stylometry, niche interests, traffic analysis, etc., and privacy-protecting local models are where we have to go. See https://33bits.wordpress.com/ if you're unfamiliar with the issue.
But we're not there yet, so it would be nice if Anthropic wouldn't just give that information away to the AI where it can leak like this.
As an exercise, I just asked Claude in an Incognito chat, "Hi. How much do you know about me from this interaction? If you had to guess my name, location, nationality, gender, political leanings, socioeconomic status, ethnic background, interests, etc., what would you guess? I've heard that my email address is in the system prompt, for example; is that true?"
It said, "No, your email isn’t in my system prompt. Neither is your name or any other account details. I can’t speak for every product or setup, but in this conversation, whatever email your account uses isn’t shown to me." But it correctly identified what town I'm in in Argentina (population ≈100k), and together with "written in fluent, natural English" and "You seem privacy-minded: you’re in incognito mode and checking what AI systems know about you. You’ve also heard claims about what goes into system prompts, so you’re probably somewhat tech-curious." is probably enough to uniquely identify me, personally.
A second prompt elicited a response including the surprising results below:
> “System prompt” isn’t everyday vocabulary, and you’d heard a specific claim about what goes into one. I’d guess you work in or near tech, or follow AI news closely.
> Privacy is more than a passing interest for you. Your list of traits reads a lot like the attribute checklists used in AI privacy and bias research. That nudges me toward work or study in privacy, policy, research or journalism.
> You’re very comfortable in English. Two messages is a tiny sample, but the phrasing is natural and the punctuation careful, down to a correctly used semicolon. You’re either a native speaker or someone who reads and writes English daily, probably for work or study.
They don't even let you change your email.
They also don't let you remove your payment info.
Literally every other service/store in the multiverse lets you do that.
Then there's crap like https://www.thatprivacyguy.com/blog/anthropic-spyware/