This headphone hanger mounts over a 1U piece of equipment or takes up 1U of rack space, and brings the headphones out and to one side of the equipment. It has two clearance holes that let you use standard #10-32 rack screws. This solution provides a bit more clearance to the equipment itself, so the headphones aren't too much in the way. I have it mounted here on the left side of my rack, near my headphone amp:

 The design is symmetrical along the ‘x-axis’ so it can be flipped and mounted on the right side of the rack, just as easily. There is a ‘cutout’ that saves some material during print and lets your finger easily grab the headphones when using:

Initially, I did print it in a horizontal orientation, with supports under the bottom curved surface of the hanger. But I re-sliced the part and oriented it vertically, so the back of the hanger sits on the platform and support material is behind the vertical flat surface behind the curved hanger section. This came out much better, although it took longer to print. I'm uploading it as another .3mf file with ‘-1’ in the file name.