TL;DR: User the server's IP address, not its (local) name.
Once the sever is configured, it's time to add it to your account. To do that, you need to open the server in the browser.
Unfortunately, Plex doesn't work very well with names (mdns). My server was named
cinema.home.lan. I could set it up first time, but subsequent attempts failed. I've looked on hte interwebs for a solution and I found that:
I need to use the server's IP address, not its name.