VS Code extension: Set terminal tab name from conversation/chat name

Feature Request

When using Claude Code in VS Code, the terminal tab defaults to a generic name (e.g., "node" or "claude"). It would be great if the tab automatically reflected the current conversation/chat name.

Current Behavior

• Terminal tab shows generic name ("node" with npm install, or "claude" with native)
• Users must manually right-click → Rename to identify different sessions

Desired Behavior

• The VS Code terminal tab title automatically updates to match the active Claude Code conversation name
• When multiple Claude Code sessions are open, each tab shows its respective chat name, making it easy to identify and switch between them

Why

When working with multiple Claude Code sessions in VS Code (e.g., one for a feature, another for PR review), there's no way to distinguish tabs at a glance without manually renaming them. Auto-naming from the conversation would significantly improve the multi-session workflow.

Environment

• Claude Code v2.1.63 (native installer)
• VS Code with Claude Code extension
• macOS (Apple Silicon)