Feature request: Allow renaming Claude Code panel tabs in VS Code

Problem

When opening multiple Claude Code sessions via the sparkle icon in VS Code, they appear as tabs in the editor area. Each tab shows the conversation's first message truncated (e.g., "you were helping me crea..."). With multiple sessions open, the tabs are nearly indistinguishable from each other.

Requested Feature

Allow users to rename Claude Code panel tabs. Possible approaches:

• Right-click a tab to rename it (similar to terminal tab renaming in VS Code)
• A command palette entry (e.g., "Claude Code: Rename Tab") to set a custom title for the active session
• An API or VS Code command to set the tab name programmatically

Use Case

Multi-agent workflows where different Claude Code sessions handle different roles simultaneously. For example, one session might be a "Builder" implementing code, another a "Reviewer" checking a PR, and a third working on a specific task like "SPIKE-0059". Being able to label each tab with its role makes context-switching between sessions practical.

Bonus

Programmatic access to set the tab name via a VS Code command (e.g., claude-code.setTabName) would allow extensions that manage multiple Claude sessions to label them automatically on creation.