And I get "GLOB(0x109ad10)" when printing "$fh" - how can I get the name of the file from $fh, not simply from "$name"

You can't, see retrieve filename from filehandle?, filenames from filehandles, Retriving Filename from Filehandle, Filename from filehandle?, https://metacpan.org/module/Path::Tiny#openr-openw-openrw-opena