If you're adding a lot—as in thousands—of images to Name Mangler's file list, it can take a while. The issue isn't Name Mangler directly, but rather the icon preview that shows a miniature version of each image file. Getting those previews from the system takes time. It's not that it's really really slow, but that it's slow enough that you'll notice it when dragging in thousands of image files.

To speed up the operation, before dragging in a large number of image files make sure View → Show Icon Preview is not checked in Name Mangler's menus.