Any way to get Lightroom to show the name of the current catalog, perhaps in the identity plate?
Lightroom Catalog name is displayed at the very top in the title bar or under Catalog Settings> General tab
You can manually mention the Catalog name under Identity Plate but it would not pick the catalog name automatically.
The filename of the catalog is shown in the title bar.
If you hover the mouse pointer over the title bar, it will show you the full path in a popup window.
OK. There it is. The title bar was not visible. Had to go to Window/Screen Mode/Normal