Persist a new robot display name and apply it live (no restart).

Persists the name to disk, then refreshes the advertised copies so the rename takes effect immediately: the daemon status + central relay (via Daemon.apply_robot_name) and the LAN mDNS record. This is the REST entry point used by the BLE setup service; the WebRTC set_robot_name command goes through the same live-apply path on the backend.