From the database window, the box that lets you select and open Tables, Queries, Forms, Reports, Macros and Modules, Select Modules and select the New button, it will open a new window where you enter VBA code that is blank except for one or two lines of code at the top.
Copy and past ChrisO's last code sample into the module and save it, the name of the module you save it as is not really important at this time, so anything will do.
Now on the Report, select the textbox that you want to display the database name, open the properties window and in the Control Source property, enter the following:
=GetCurrentDB("FullName")
now save and open the report and the report should now display the database name in the text box.