I think it would be helpful if the custom report designer allowed users to insert into the report the name of the user-defined group used as its data source. To me, it is very helpful looking at a report if you know where the data came from. If a user chose to add in the user-defined group name as data source, it could appear as a subtitle (perhaps) or somewhere in the footer (perhaps) or at a user defined location within the report using the existing custom report designer.
This is important because a report doesn't necessarily list all data in the database within the report parameters. For example, a report showing death dates for a particular population could show all people who died in a location, or it could show a 10-generation family group, or whatever. The people in the report would differ according to the data source.
Of course, this would work only if a user-defined group was used - but I think it is a helpful idea.