Does anyone know what would the color is for the cleaning rod end on the Panzer IV H/J? Is it a piece of rag or what? what is the correct name for it?

Jody, the brushes I clean my guns with start out white but after a few cleanings they turn a sooty black with some of the white color still visible.

You could use rags pushed through the barrel but I believe they used bore brushes.

In the stowed position on the Panzer IV the brush head was covered in a canvas case.

To directly answer your question - any Khaki color will do.