SSRS email subscription with custom file name on the attachment
This is the first way I could think of to make this happen: 


Create a data-driven subscription for the report
Specify Windows File Share as the delivery method (this would imply that you had a file share location available)
Connect to a data source
Write a query to generate the name 
Specify that name as the report name in the location of your file share
Have a process by which the end-users are emailed this report - perhaps a SQL Agent job? 


As a matter of personal exploration, I wonder if it'd be possible to modify the SQL Agent job that the subscription creates such that you could add a step to send the file via email.