[FEATURE] Allow renaming session titles in 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

Session titles in the Claude Code VS Code sidebar are auto-generated and cannot be renamed. As sessions accumulate over days/weeks of work on a project, it becomes very difficult to find specific conversations. I end up opening multiple sessions just to check which one had the debugging work vs. the refactoring work.

Proposed Solution

• Right-click on a session title in the sidebar → "Rename" option
• Or double-click the title to edit inline
• Custom names persist across restarts
• Original auto-generated title shown as tooltip/subtitle

Alternative Solutions

Currently I have no workaround — I just scroll through sessions and try to remember which auto-generated title corresponds to what work. Sometimes I open 3-4 sessions before finding the right one.

Priority

Medium - Would be very helpful

Feature Category

Interactive mode (TUI)

Use Case Example

1. Working on a project over several weeks
2. Accumulate 15+ sessions for different tasks (bug fixes, new features, refactoring, debugging)
3. Need to resume the "database migration" conversation from 3 days ago
4. Currently: scroll through 15 auto-generated titles like "Help me fix...", "Can you update...", guess which is which
5. With rename: sessions labeled "DB Migration", "Auth Refactor", "Bug #42" — find it instantly

Additional Context

This is a common UX pattern in chat-based tools (ChatGPT, Cursor, etc.) where users can rename conversations for organization.