I've never had a problem changing a router's SSID via WiFi before, obviously the connection will drop but you simply scan for the new network name and reconnect.
Re: Changing SSID
Thanks for the info.
Would have tested things myself today but OpenReach failed to show up to do my FTTP connection. While I use a wired connection my neighbour uses WiFi (and will need to change things if OpenReach show up tomorrow!!!).
Waiting to hear what happened to my appointment.