Allow renaming conversation tabs in VSCode extension

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

When using Claude Code in VSCode with multiple conversation tabs open, there's no way to rename them. All tabs have generic names, making it hard to tell which conversation is which.

Request: Allow users to rename conversation tabs (e.g., double-click to edit, or right-click → Rename).

Proposed Solution

When working on multiple tasks in parallel, meaningful tab names like "fix auth bug" or "refactor API" would make switching between conversations much faster.

Alternative Solutions

_No response_

Priority

Medium - Would be very helpful

Feature Category

CLI commands and flags

Use Case Example

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Additional Context

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