1. First, create a custom field on your Custom object or Standard object. Or you can choose an already existing field for the object.
  2. Search for the tab Excluded Object. 
  3. If you cannot find it, proceed to the next step, otherwise skip to step number 5.
  4. Go to the Setup and search for "Tabs" in Quick Find. Click on "Tabs" and create a new "Tab" for the object excluded object (Namespace: DownloadFiles). Follow these steps to create a tab: Salesforce Help to Create a Custom Object Tab
  5. Go to the excluded object -> Create a ListView "All" and add Excluded Object Number, Object API Name, and Folder Name as the three fields in the list view as shown in the screenshot.
  6. Hit save. Look for the object for which you want to change the folder name. Edit that record's folder name with the newly created formula field (API Name) as shown in the screenshot. Then click the save button. 
  7. Now go to the MFD tab/ Lightning Component and refresh it. You can now download the files with the newly set folder name.

Note - The functionality of renaming folders and file names will not be applicable when you select an object as Attachment or File on the Mass File Download tab. Select Object = Attachment or File functionality is available from v12.0 onwards.