I donot think there is any direct way to get name of drawable image unless you stores the image name along with image.
In XML you can do the following to set image name as an additional data to imageview
android:tag="btful.png"
Programmetically setting imagename
ImageView img = (ImageView) findViewByID(R.id.img)// my image
img.settag("btful.png"); // to set an image name
you can get the image name by using getTag()
String imageName = (String)img.getTag();
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