Hello and welcome!
You are correct in assuming that Projects expect a consistent file name for reports. The kind of functionality you're looking for exists in Monarch's "big brother", Data Pump.
But, if want to give a little programming a try, you should be able to get this done yourself.
Read over this [url="http://mails.datawatch.com/cgi-bin/ultimatebb.cgi?ubb=get_topic;f=1;t=000568;p=1#000001"]previous post relating to dates in file names[/url] for inspiration.
Let us know if this sheds any light on your problem, and how you make out.