It seems that the only Layout Style that allows you superimpose a file name (or other text) onto the images in the Print Module is the "Single Image / Contact Sheet". If you use that option instead of "Picture Package" the images will be either a single image per page or a grid of images with a consistent number of rows and columns (like a contract sheet if you're old enough to remember those from film). In this layout style, go down to the ":Page" panel and check the "Photo Info" box near the bottom of that panel. Then select "filename" from the pulldown list. Below that you can select a font size. The info prints under each image.
Hope that helps
Yes the Print module does have the limitation that you cannot print metadata ON the area of the image. But you can create any multiples of metadata to show BELOW the image area as "Photo Info".
To locate the Filename (or other metadata) actually ON the image (as you would a watermark) you will need a plugin like "Mogrify" https://www.photographers-toolbox.com/products/lrmogrify2.php?sec=quickguide
And for Picture Package- Nothing!!! Not possible.