You can create as many Reports as you'd like from a Data Source. Reports are saved instances of your Data Sources and their selected settings.
To indicate details about the selected Report settings in the Report Name, select the "Add a Name Format" option. You can then dynamically output any value from your Report settings in the name of your Report using Craft Object Syntax.
In the following example, the Start Date and End Date values are included in the Title of the Report. When published, the Report Name would appear with the selected dates: