I keep a back scratcher at my desk (dry skin = itchy back) and got tired of it being in the way, so I made a simple hanger to hang it off the back of my monitor. It's just a simple hook with a gap in it for the handle. Printed in PLA at 0.32mm layer height with 2 perimeters and 3 top and bottom layers. I printed it on its side and I did use supports for the “top” hook.

As usual, I'm including the FreeCAD file, so feel free to tweak things to fit your own needs.