I’m not aware of an “easy” way to do this within the connector itself, but what we’ve done previously is use a PowerShell script running via the Windows Task Scheduler to be a basic file renamer/archiver. Basically the script kicks off once an hour and looks for a predefined set of filenames for various sources that match a configured naming scheme. If it finds a file it creates an archive/backup based on a defined format (i.e. sourceName+date) and then creates a copy with the standard filename the connector is configured for.
This allows us to use a configuration file with the PowerShell script for basic renames and we can deal with daily files generated by other sources.