Hi there,
So yes, Google Apps Scripts can solve your problem.
It seems to me that you want a solution that is valid across your domain, such that the script can update the names for Google Docs used by your domain members.
We can create a Google Apps Script and deploy it as a web app accessible by your domain users, then each user wants the script to be effective inside his Drive, he can open the app and authorize the script to access their Drives, then the script will run using a time driven trigger every 5 or 15 minutes, scan the Drive for all Google Docs files and update their names based on the last updater, last update date and author.
This is the best workflow I have thought of that will be suitable to your case.
I will be happy to address any of your questions!
Sincerely,
Mohamed