You can use Lightroom’s file naming tools in the Publish Service. This will rename files as you upload to MediaGraph. In general, it’s best to not rename, so that the files in Lightroom will have the same names on MediaGraph.
Add Copy name if you use Virtual Copies
If Virtual Copies are a part of your workflow, you can add the copy name automatically to the filename, whenever a copy is uploaded. (Files that are not virtual copies will just have the filename.)
Open the File Template Editor and make a new preset that includes File Name and Copy Name.