You can configure an Event Rule triggered by a Folder Monitor Event to copy or move files in the folder and save them with a different name. Refer to Copy/Move File to Host Action for details of defining an Event Rule using the Copy/Move file to host Action.
%FS.DST_PATH% instead of %FS.PATH%
%FS.DST_FILE_NAME% instead of %FS.FILE_NAME%.
If the file is renamed, the new name context is lost to FS.PATH and FS.FILE_NAME, which retain the old path/name, but the new path/name is passed to %FS.DST_PATH% and %FS.DST_FILE_NAME%.
For example, suppose the monitored folder contained a file called Robert.txt and you rename the file Bob.txt.
%FS.DST_FILE_NAME% contains the new value Bob.txt, but %FS.FILE_NAME% contains the old value Robert.txt.
For details of the Copy/Move Action, refer to Copy or Move File to Host Action.
The client offload/download RENAME and the Folder Monitor RENAME are two different events/stimulus. The Folder Monitor RENAME uses the DST variables, whereas the client download/offload RENAME uses the SOURCE FILE NAME-related variables.