Question: Can I change the name of the actual database, not just how the name appears in the database window?

 

Go to the database window. Here you should see all the your databases listed. When you Start your ChessBase, the first screen you'll see is the database window. In many ways this screen is your "desktop" for using your ChessBase program.

 

In ChessBase select -> Tools -> Database -> Rename Files.

 

 

This open the dialog window which will let you enter the new name of the database.