It should be possible to rename sub categories of a rest service layer in ArcMap.
Example: If I add https://www2.env.go.jp/eiadb/arcgis2/rest/services/category02_07_02_201805/Mapserver to ArcMap, I encounter an issue with renaming the different subcategories of the layer. As you can see in the attachment “category02_07_02_201805” could be renamed in “Natural environment”, but 国立公園 etc. could not.
Even if I open the layer properties, it seems to be read-only and I cannot type in a new layer name.
I can rename the same layer in another opensource software, so it is not protected from the server-side as such.
It is very unfortunate that a functionality of an Esri-designed ArcGIS service is not working in ArcMap, but does in an open source software, so please address this issue.