Hook it over your desk edge, push the hanger up until it clicks snug, done: no screws, no bolts, no drilling. A two-rung ratchet locks it every 4 mm, and a leaf spring built into the top jaw takes up the gap between clicks, so it sits tight on any desk top from 12 to 40 mm thick. To move it, pull the little tab towards you and slide it off. It prints as two parts with no supports and no hardware, and it holds your headphones under the desk on a wide 56 mm saddle with a rear lip.

Print both parts lying on their side, exactly as oriented in the STL files: PETG recommended, 0.2 mm layers, 3 walls, 15% infill, no supports (about 3 h and 35 g in total). To assemble, slide the slider onto the spine from below with the finger tab facing you.

Designed and checked in CAD. The spring and click forces are calculated, so I'd love to see your makes and hear how it fits your desk!