Can't Rename Pages Template
First, I'm using a Late 2013 iMac 27" using Mojave 10.14.6 and Pages 10.1 (I have sitting here a new iMac, still in the box which I will be migrating to. It's going to be painful to lose the big screen, and the resolution on this 27" iMac is all I really need.)
I found my own solution to this problem. After you create a new template in Pages and save it using: File / Save as Template… and selecting Add to Template Chooser. It is saved in the template chooser with a title Untitled n.Template (n being a sequence #). To rename it, first CNTL-click on the Untitled name. Then type in the new name. Now click the mouse off the template icon and it will be renamed. If you hit RETURN instead, the Template will not be renamed, instead either Pages in my case will often crash, or the Template name will revert back to Untitled n and the Template will launch.
iMac 27″, macOS 10.14