For obscure reasons, I have a pair of headsets attached to the PC: one USB that’s used for phone calls and one plugged into a sound card for everything else.
They’ve been cluttering up the corner of the desk for far too long, so I bent up a rack from a surplus coat hanger. Nothing critical, as long as it’s tall enough to hold the mics off the desk and wide enough they don’t clunk together.
The trick is to just drill a hole in the top of the desk and poke the end of the rod into it. That works because my desk has a notch along the edge just exactly the right width to hide the hole!
Maybe you don’t want to do this to the top of your desk, in which case maybe you can bend the hanger around the edge and put a screw in the bottom or the desktop. If you don’t look under there very often, the spiders will take over; this one is from the basement desk that I haven’t used for far too long.
Details of the hanger, not that you can’t figure it out on your own:
I suppose you could actually buy these things…