/rename does not propagate to how the session appears in ListAgents on peer sessions

Description

Renaming the current session with /rename <new-name> confirms locally
("Session renamed to: <new-name>"), but other concurrently-running Claude
Code sessions on the same machine do not see the updated name when they
call ListAgents (or the /list-agents slash command) — they keep
showing the old name indefinitely.

Steps to reproduce

1. Start two Claude Code sessions (A and B) on the same machine, in

separate terminals/tmux windows, so they can see each other via
ListAgents.

1. In session B, call ListAgents (or /list-agents) and note session

A's displayed name.

1. In session A, run /rename some-new-name. Confirm the local response

acknowledges the rename.

1. In session B, call ListAgents again.

Expected behavior

Session B should see session A listed under some-new-name (perhaps
after a short propagation delay).

Actual behavior

Session B continues to show session A's old name. Repeating the
ListAgents call several times over several minutes shows no change —
the rename never propagates to peers, even though the renaming session
itself confirms the change took effect.

Environment

• Claude Code CLI (interactive sessions), Linux, tmux-based concurrent

sessions on the same host.