Unless somebody more knowledgeable corrects me on that, your best bet would likely be to have a --run-script-after parameter that uses a batch file to rename the log.
If you do go that route, remember that you get to variables like the backup name (which would be %DUPLICATI__backup_name%) as described here:
Of course you’ll need to be careful you don’t give your backup a name that can’t be used in a file name (so skip using *:/\ etc.).