Good day to you johnnyjackhammer,
Are you able to edit the location name for other’s locations in the Find My app, such as your location? You mentioned seeing the name change you made on your Mac reflect on your iPhone. Are you able to edit the location name from another device and have it show on your Mac? That would let us know if the issue exists only when originating on your Mac.
You mentioned having restarted was that the app, your Mac or both?
Are these the steps you’re taking? Locate a friend in Find My on Mac
Click the Info button on the map, then do any of the following:
Label a friend’s location: Click Edit Location Name, then select an option (such as Home or Gym), or click Add Custom Label, enter a name, then press Return.
The label appears below your friend’s name instead of the location information.
Thanks.