This same problem exists in Excel Client as well when looking at multiple variables with the same classification names. For example, if you have a prop and an eVar that have the same classifications, it will display the same name in Excel Client when choosing a report.
As of our last maintenance release, classifications in the Data Warehouse "Breakdowns" selector are associated with their base report with names such as: Date (Traffic - Day Parting (prop15)) Date (Day Parting (eVar17)) Thanks for submitting your idea.