How can I cover a metal hanging rod?

The only thing I can think of is removing the rod and sliding PVC piping over it. The printing on the pipe will show though. I can't recommend painting the PVC because it would eventually scratch off....unless there is a strong epoxy coating that you could protect it with after painting the PVC your color of choice. Hmmm...

I've used contact paper. It comes in many colors and patterns. Will last several years before it needs to be replaced. Hangers slide better than on the metal.

I have seen closet rod covers in hardware stores - they're basically a very thin plastic tube with a slit running down the side. https://www.homedepot.ca/en/home/p.shower-rod-cover---white.1000111409.html

...or you can replace it with a wooden dowel cut to length. If you want smaller diameter rod install two new supports, all you need is a drill with screwdriver bit. If rod is over 6" install a support in the middle; they're available at any home improvement store. Easy quick fix & wood is much nicer than metal, I think. ;~)

...6 feet...

wrap contact paper from dollar store...pattern your choice...coat with varnish...hangers will slide easy on the glossy surface...or instead of varnish you can use triple thick glaze (that is the real name)...look it up on the internet....or paint to suit your taste---then glaze or varnish

We bought a white plastic "slip cover" that was intended / marketed to cover a shower curtain rod (Depot or Lowes, can't remember which). Was only a couple of bucks. 👍

I had the same "metal pipe" in my closet. I bought some spray paint for automotive use. Tractor & Implement spray paint would work too. I took out the rod, stuffed the inside with crumpled newspaper (deadened the sound of my oak trouser hangers on the rod) then sanded with some 220 just to remove any dirt & debris. Sprayed three light paint coats on a 90 degree day, then left it to "cure" another 2 days. The pipe rod was quieter, and I loved my bright red "wow" when I opened my closet!!