As I said, but maybe not clearly, if you use
BMAP* picture = "image.bmp";
PANEL* panel = { ... bmap=picture; ...}
then there is NO way to get the filename of the original bitmap
through the panel, the filename just isnt stored anywhere.

But if you use PANEL* panel = { ... bmap="image.bmp"; ...} then you can get it back with
STRING* filename = str_create( mainpan->bmap->link.name );
(filename.chars)[str_len(filename.name)-4] = 46;