Allow renaming Claude Code chat tabs in VS Code

Problem

When multiple Claude Code conversations are open in VS Code, the tab names are auto-generated from the first message (e.g., "Czech language acknowled...", "Ahoj. Dívám se, že ve Wi..."). This makes it impossible to distinguish between conversations at a glance.

Current behavior

• Tab names are derived from the conversation's first message
• Names get truncated and look cryptic
• No way to rename or customize tab titles
• With 3+ conversations open, it becomes very confusing

Proposed solution

Allow users to rename Claude Code chat tabs — either:

• Right-click → "Rename Tab" on the conversation tab
• A pencil icon or inline rename option
• Or a /rename command within the conversation

Why it matters

This is a basic UX expectation. Every browser, terminal, and most IDE tools support tab renaming. Without it, managing multiple conversations is frustrating and not user-friendly.