[FEATURE] Add the ability to manually rename conversation titles in the Claude Code VS Code 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

Current Behavior
Conversation titles are automatically generated based on the content
Users cannot manually edit or rename existing conversation titles
No rename option available in the conversation list context menu or UI

Proposed Solution

Allow users to rename conversations through one or more of these methods:
Right-click context menu: Add a "Rename Conversation" option when right-clicking on a conversation in the sidebar
Inline editing: Allow users to click on the conversation title to edit it directly (similar to file renaming in VS Code)
Keyboard shortcut: Support F2 key for renaming (consistent with VS Code's file rename behavior)
Edit icon: Show an edit/pencil icon when hovering over conversations

Alternative Solutions

_No response_

Priority

High - Significant impact on productivity

Feature Category

Developer tools/SDK

Use Case Example

1. Organizing conversations by project or topic
2. Adding custom labels for better searchability
3. Maintaining cleaner conversation history
4. Distinguishing between similar conversations

Additional Context

This feature would improve conversation management and user experience, especially for users who maintain multiple ongoing conversations across different projects.