Remote Control: session name prefix lost after auto-rename, no machine identifier shown

Problem

When using --remote-control-session-name-prefix to distinguish sessions from different machines, the prefix is lost as soon as Claude auto-renames the session based on conversation content. Additionally, the remote control session list in claude.ai/code and the mobile app shows no machine/hostname identifier, making it impossible to tell which machine a session is running on.

Use case

I run Claude Code sessions on a headless Mac mini via a mobile app (SSH + tmux). I also run sessions on my laptop. When I open claude.ai/code, all sessions are mixed together with no way to tell which are on the mini vs. my laptop. They all just say "Remote Control."

Current behavior

1. Start Claude with --remote-control-session-name-prefix mm-MyMachine
2. Session initially appears as "mm-MyMachine: <auto-name>"
3. After sending a message, Claude renames the session and the prefix is dropped
4. In claude.ai/code, all remote sessions look identical — no hostname, no machine identifier

Expected behavior

Either:

• Persist the prefix through auto-renames (e.g., always show "mm-MyMachine: <conversation name>")
• Show the machine name in the session list (the machine_name field is already sent during POST /v1/environments/bridge registration)
• Both — prefix + machine name would make multi-machine setups immediately usable

Environment

• Claude Code v2.1.92
• macOS (headless Mac mini via SSH + tmux)
• Remote control auto-enabled via /config