Display file name within Image Browser

It would be helpful to display an image's file name below the image within the Image Browser. One site I have this on has many similar images, and the file name would be useful in distinguishing them.

I tried adding the file name to the fields in the view, but that didn't cause it to appear, so I guess there's some theming that would need to happen.

I'm neutral about whether the file names should be displayed by default, but at least it would be nice to support the ability to add the field in the view and have it displayed.