Feature request: Auto-summarize remote control session names

Summary

When "Enable Remote Control for all sessions" is on, sessions appear in claude.ai/code with generic or first-message-derived names. For users managing multiple concurrent sessions, these names are not descriptive enough to identify what each session is doing at a glance.

Current behavior

Session names are derived from:

1. An explicit --name or /rename (manual, static)
2. The first user message (auto-generated once, never updated)
3. A hostname-word-word fallback

After a session has been running for a while, the initial name often no longer reflects what the session is actively working on.

Proposed behavior

Periodically auto-generate a short summary title (1-5 words) from the conversation context and update the remote control session name. This could be triggered:

• After every N turns or on detected topic shift
• Using the same lightweight generateSessionName call that already exists for terminal tab titles

Why this matters

With remote control enabled globally, the session list in claude.ai/code and the Claude mobile app becomes a primary way to monitor and switch between sessions. Descriptive, current names are essential for this workflow.

Related issues

• #37349 — Dynamic session labels (broader scope: in-terminal labels + color coding)
• #45979 — --name flag being overwritten (bug)