Add a "Streamer/Privacy" mode to hide name, email, and org from the startup banner

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

When launching claude, the startup UI shows personal information: a greeting with the account holder's real name ("Welcome back Jon!") and an organization line containing the account email ("jon.doe@…'s Organization"). For anyone who streams, records tutorials, screen-shares, or presents Claude Code publicly, this leaks PII the moment the tool starts.

Proposed Solution

A supported way to suppress or mask this info, e.g. any of:

• A privacyMode / streamerMode flag in settings.json, or a --privacy launch flag
• An env var (e.g. CLAUDE_HIDE_ACCOUNT_INFO=1) to omit the greeting and org lines
• Optional display-name / org-name overrides in settings so shown values aren't the real name/email

Alternative Solutions

Launch off stream on a second montior and press Ctrl+L to clear the banner before moving to the shared screen. This works, but easy to forget and adds extra steps.

Priority

Medium - Would be very helpful

Feature Category

CLI commands and flags

Use Case Example

I would enable it by default so it never shows PII in the banner, then I would not have to remember and worry about accidently leaking PII when streaming.

This affects a growing group of content creators, educators, and conference speakers demoing Claude Code. A one-line toggle would remove a real, recurring privacy footgun.

Additional Context

_No response_