Is there any way to list the filename of the image (excluding extention) under the image.

Perhaps there is a hack or another theme or some switch or plugin that I haven't found.

Thank you.

You can use something like this:
``

We also have a function to strip the suffix :-) :
echo stripSuffix( $_zp_current_image->getFileName() );

In any case you need to modify the theme used.

Thank you. I will give it a try.

Which file would I modify with those statements?

You did read the theming tutorial, didn't you? album.php or image.php depending under which image you want to show the file name and also of course if the theme used follows the standard structure.