|"We want to do this as an additional option before we disable the old one" |
I assume by a "new name" in your post you mean a pass phrase (or key). Whatever you cannot have one network with another name or pass phrase. You would have to set up am additional network, if you server allows this.
The best way therefore is to reset the router and start over. Mostly these days both the network name and pass phrase are on a sticker either at the back or underneath the router. It will be necessary to set each device to match whatever you use.
Always pop back and let us know the outcome - thanks