Strategy Web allows users to rename the actual history list message on their inbox, without renaming the original report, as described in KB20866: How to Rename History List Messages in MicroStrategy Web 9.0.
The history list message in Strategy Web can be renamed to a maximum of 255 characters including spaces. Any character after the preset limit will be automatically cut off.

However, even though the history list message can be renamed to a 255 character name successfully, if the user wants to save this renamed report after running it, Strategy has a 250 character limitation for saving report names, and will see the following message:

Therefore the maximum limit in general that a report's name can be set to is 250 characters.