You could try using split:
Split($feature.labelfield, ' ')
I haven't used this one much, but if I read correctly, the first set of quotes with the space between will tell the Arcade renderer to use spaces as splits. You can also add a comma and then give it an integer value to specify the maximum number of splits.
Split($feature.labelfield, ' ', 1)
That might be helpful because it will for sure remove "County" from the return, but it might give you problems if a county has a two word name (ex. Otter Tail County" would just return "Otter.")
https://developers.arcgis.com/arcade/function-reference/text_functions/#split
Another option might be something like this:
var txt = $feature.labelfield;
return Left(txt, Count(txt)-7)
If all the names are the same (County, which is 6 letters, plus a space before it) this should remove the final 7 characters of each name. This expression came from a similar ask on the community
PS sorry for a bunch of edits, I had ideas right after I hit submit!