If you have selected files in Copywhiz using File Explorer (Windows Explorer), then go to the destination folder. Right-click inside the folder, choose Copywhiz → Paste Advanced to open the Copywhiz window and click on the 'Advanced Settings' button as shown in the picture below.
If you have Copywhiz's main window already open, then you can directly click on the 'Advanced Settings' button as shown in the picture below.
Now, click on the drop-down, as shown in the picture, and click on either 'Rename source file' or 'Rename destination file.' Plus, you can provide a file name suffix to easily identify the exact files renamed during a file copy batch.
Press the OK button and click on the 'Paste Now' button to copy the files with auto-renaming of duplicate files enabled. A sound plays indicating the successful completion of a file copy task.