Thank you for the nice question, Matthew.
The default name of the file, when exporting a report, is the name of the report class plus the appropriate extension. As of now, there is not way to override that name at runtime. You can create different report classes with different names that inherit from your original report, and each of them will be exported with its appropriate name.
We will consider adding this functionality in a future version. There is no workaround I can suggest at the present moment.
the Telerik team