Neither UIImageView not UIImage holds on to the filename of the image loaded.
You can either
1: (as suggested by Kenny Winker above) subclass UIImageView to have a fileName property or
2: name the image files with numbers (image1.jpg, image2.jpg etc) and tag those images with the corresponding number (tag=1 for image1.jpg, tag=2 for image2.jpg etc) or
3: Have a class level variable (eg. NSString *currentFileName) which updates whenever you update the UIImageView's image