Is there a way for WP media library to display image names during selection?

Does anyone have any idea if the WordPress media library can display the names of the images that you load in it — when you are in the selection process for a post or featured image? I have about 400 images and they appear to be organized in alphabetical order, which is great, but there are no names.

I tried NextGen gallery, which is a great plugin, but for some reason, although the names are shown, the images are not in any particular order — just random. Also, the small window that they are displayed in is just too small.

I would just as soon use the default media library for this particular website that I’m working on, as it would eliminate a plugin and would also be easier for the person I’m teaching.

Any help would be most appreciated.