[FEATURE] `/rename` should update the VSCode tab header with the new session name

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

/rename should update the VSCode tab header with the new session name

Current behavior

After running /rename My New Session Name:

• The session name updates internally (visible in session list)
• The VSCode tab header continues showing the previous/default name

Proposed Solution

Feature request

When using /rename My New Session Name in the Claude Code VSCode extension, the session is renamed internally but the VSCode tab header does not update to reflect the new name.

Why this matters

When working with multiple Claude Code sessions in separate tabs, the tab header is the primary way to distinguish between them. If /rename doesn't update the tab title, the rename is effectively invisible during active work — you have to close and reopen or check the session list to confirm which session is which.

Environment

• Claude Code VSCode extension
• macOS

Alternative Solutions

_No response_

Priority

Medium - Would be very helpful

Feature Category

Developer tools/SDK

Use Case Example

Expected behavior

After running /rename My New Session Name:

• The VSCode tab header should immediately update to display "My New Session Name"

Additional Context

_No response_