In KDE or Plasma or whatever they're calling it now, programs on the panel show the name as well as the icon. I would like to hide the name so it just shows the icon but I couldn't find how to anywhere.
The default Panel in KDE Plasma Desktop is a widget container.
I suppose the list of icons/names you are referring to is the "Task Manager" widget. It appears not to be configurable to show icons only. You will have to choose a different widget instead.
Thanks to this forum thread: right click on the Panel, click "Unlock Widgets", right click on the Panel again. You should get a drop-down list that includes "Alternatives", one of which is "Icons-only Task Manager".