[FEATURE] Expose /rename (session display name) in VS Code extension native UI

Summary

The /rename slash command — which sets a session's display name (used in the /resume picker and terminal tab title) — appears to be available only in the terminal (TUI) mode of Claude Code. It is not exposed in the VS Code extension's native UI input box.

Please surface /rename <name> in the native UI input so VS Code users can rename the current session without having to switch to terminal mode.

Current Behavior

• In TUI / terminal mode: typing /rename foo works and the session display name updates (shown in /resume picker and terminal tab title).
• In VS Code extension native UI (the chat input box, with claudeCode.useTerminal: false): /rename does not appear in the slash-command autocomplete list, and typing it manually has no observable effect on the session name.

Other built-in slash commands (/clear, /compact, etc.) are exposed in native UI, so the omission of /rename seems incidental rather than intentional.

Expected Behavior

/rename <name> available in the native UI input box, with the same effect as in TUI mode:

1. Updates the session display name (visible in /resume picker / --resume <name> matching).
2. (Optionally) updates the terminal tab title, respecting the existing terminalTitleFromRename setting.

Why This Matters

The CLI flag -n, --name only works when starting a new session. Once a session is in progress in the native UI, there is currently no way to rename it without:

• Switching to terminal mode (useTerminal: true) just to run the command, or
• Editing JSONL session metadata files directly under ~/.claude-team/projects/.../.

Both are unnecessary friction for a feature that already exists in the same CLI.

Environment

• Claude Code VS Code extension: 2.1.145 (also installed 2.1.147)
• VS Code on macOS (Darwin 25.3.0, arm64)
• Verified by inspecting the bundled extension.js:
• Setting schema includes terminalTitleFromRename with description "Whether /rename updates the terminal tab title (defaults to true)..." — confirming /rename is a first-class CLI concept.
• contributes.commands in the extension's package.json contains no rename-related command (reopenClosedSession is the only "session" entry).

Suggested Implementation

Either:

• Route /rename in the native UI to the same handler the TUI uses, or
• Add a VS Code command (e.g. claude-vscode.session.rename) that prompts for a name and calls the same handler, so users can also bind a keyboard shortcut.

Thanks!