Step 1:  Click on the database name with left mouse button to edit.  This highlights the name and brings the cursor into edit mode.

Step 2:  Type in new name for database.  Avoid using apostrophe's or any characters that might cause trouble with windows directory system.  You don't need to enter ".mdb" extension.

Step 3:  Hit enter to accept the new name.  This will prompt you with a confirmation dialog box.  Confirm the change by clicking on Yes button.