You may just need to copy the file name and paste it on your print sheet. Inconvenient but it should work and you can choose where to print the file name along with choice of typeface, size, color....
I use a template for my master prints which includes a place for my caption and my signature & copyright slug, both below my image area. However, I have different templates for different aspect ratios and vertical/horizontal.
My collection of templates is sized for my normal portfolio print which is printed on my large-format printer, about 24x18 sheet size (using roll paper). From this master I usually print smaller prints to start, usually on 8.5x11 paper so it's just a matter of changing the size of the image in the print dialog: 50% on 8.5x11, 70%-78% on 13x19, 100% on the 24-inch rolls. This covers about 97% of all my printing.
Using a template for print output and copy/pasting the file name onto the template along with your image may be your best bet unless someone knows of another (automated and easier) way which is somewhere above my pay scale.