[BUG] Conversation name lost in active session after /resume, despite showing in picker

Bug Description

After renaming a conversation with /rename, the name persists in the /resume picker list but is not loaded back into the active session when you resume that conversation.

Steps to reproduce:

1. Start a new Claude Code session
2. Use /rename MyConversation to rename it
3. Verify name is set (via /status)
4. Exit the session (/exit or Ctrl+C)
5. Run claude --resume or /resume
6. Select the conversation - it shows "MyConversation" in the picker list
7. Check /status after resuming - the name is no longer "MyConversation"

Expected behavior:
The conversation name should be restored when resuming, matching what's shown in the picker.

Actual behavior:
The name appears in the resume picker but is lost/not loaded into the active session after selection.

Environment Info

• Platform: macOS (darwin)
• Terminal: iTerm2

Related Issues

• #11554 - Similar but about terminal title, not /status display