[Feature Request] Auto-generated session titles should populate explicit session name in prompt bar

Bug Description
Title: Allow auto-generated session titles to populate the explicit session name (prompt bar)

Description:
Claude Code already auto-generates a session title from the first prompt (async, Haiku-class), which shows in the session picker (/resume) and the statusline's session_name field. However, this auto-title is disconnected from the explicit session name that appears in the prompt bar — that field stays blank unless the user manually runs /rename <name> or starts with claude -n <name>.

This means every new session has an unnamed prompt bar by default, even though Claude Code already has a good candidate name sitting in the auto-title system.

Requested feature (either would solve it):

1. A config flag (e.g. "autoPromoteSessionTitle": true in settings.json) that copies the auto-generated title into the explicit session name once it's ready, so the prompt bar reflects it automatically — same as if the user had typed /rename <generated title>.
2. Or, expose a hook output field (e.g. sessionName on SessionStart/a new SessionTitleGenerated event) that lets a hook script set the explicit name programmatically, so users can build this themselves.

Why it matters: Right now there's no way to get a meaningful name into the prompt bar without a manual step every session — auto-naming is 90% of the way there but doesn't close the loop.

Environment Info

• Platform: darwin
• Terminal: ghostty
• Version: 2.1.226
• Feedback ID: 67a66a59-d440-4e6f-8728-9d25bc134510

Errors

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