VS Code: allow renaming/auto-naming chat tabs

Problem

When working on multiple tasks in parallel in VS Code, all chat tabs show the generic name. It's impossible to distinguish between conversations without opening each one.

Proposed solution

1. Allow manual rename — right-click tab → Rename, or double-click tab title

Use case

Working on a large project with separate concerns: security audit in one tab, infrastructure setup in another, mobile client in a third. Currently all tabs look unintuitive, requiring mental tracking of which tab is which.

Environment

• Claude Code VS Code extension
• macOS