Modify 'Display template' field for Person table

You will need "%" around the FK as well. (%FK(UID_Department).DepartmentName%)

It didn't help. Now it shows % instead $ but no DepartmentName

Yep, sorry, you need both. (%$FK(UID_Department).DepartmentName$%)

Nope. Now it shows:
John Doe (%$FK(UID_Department).DepartmentName$%)

Solution is much simpler. It should be "%FirstName% %LastName% (%UID_Department%)"
Now it works

Yes, starting with version 7 we introduced the option to get the Display value of a foreign key using the same %-syntax as for the other properties.

Please be aware that this comes with a slight performance penalty, when are loading lists containing that kind of display for it's items.

If you want to avoid that, use a template for another column, let's say CustomProperty01, and create your display as needed.

$FirstName$ $LastName$ ($FK(UID_Department).DepartmentName$)

You can than refer to %CustomPropert01% in your display pattern and are avoiding the performance hit.