Allow users to rename conversation tabs in VS Code extension

Problem

In the VS Code extension, conversation tabs are auto-named based on content and cannot be renamed. Previously, the tab name was derived from the first line of the chat, which gave users control over the label.

Now, if I start a conversation about daily tasks but mention a blog post, the tab gets named "Marketing Blog Post" or similar - making it impossible to distinguish my daily session tab from project-specific ones.

Impact

Power users running multiple concurrent conversations (daily standup, project work, content pipeline) cannot tell tabs apart at a glance. This causes confusion and wastes time switching between the wrong tabs.

Requested solution

1. Allow manual tab renaming - right-click or double-click to rename, like terminal tabs
2. Or restore the old behaviour where the first message determined the tab name, so users could type a deliberate label as their opening line

Either approach gives users control back. The current auto-naming removes agency without adding value.

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Submitted on behalf of a daily Claude Code user running 3-5 concurrent sessions.