Agent name lost when session continues from context compaction

Description

When a Claude Code session runs out of context and is continued into a new session (context compaction), the agent name assigned via the rename feature disappears. The name is no longer displayed on the right side of the screen.

Steps to reproduce

1. Start a Claude Code session
2. Rename the agent using the rename feature
3. Verify the name displays on the right side of the screen
4. Continue working until the session runs out of context and is auto-continued
5. The agent name is gone — no longer displayed

Expected behavior

The agent name should persist across context compaction / session continuation.

Actual behavior

The name is lost and not carried over to the continued session.

Environment

• Claude Code v1.x (CLI)
• macOS Darwin 24.6.0