[Feature Request] Add option to hide account info from welcome screen

Bug Description
Feature Request: Option to hide email/account info from welcome screen

When launching Claude Code, the welcome screen displays my email address and organization name. I'd like an option to hide this information for privacy reasons (e.g., when screen sharing, recording tutorials, or streaming).

Suggested implementation:

Add a setting in ~/.claude/settings.json:
{
"hideAccountInfo": true
}

Or more granularly:
{
"welcomeScreen": {
"showEmail": false,
"showOrganization": false
}
}

Use cases:

• Screen sharing during pair programming
• Recording video tutorials
• Live streaming coding sessions
• General privacy preference

This would allow users to keep their personal email private while still using Claude Code publicly.

Environment Info

• Platform: linux
• Terminal: alacritty
• Version: 2.0.73
• Feedback ID: 44e8e7aa-8578-4d5e-943e-d9421a71eb63

Errors

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