That's where a person's knuckles have literally rubbed the finish off the ceiling or panel, as they've twisted on that knob.
No, it's not possible to tell what type of finish it is from photos. I could tell with a personal inspection
, as could any experienced finisher.
The finish in this area is gone, so you have to feather the surrounding area back, removing all of the flaking material and then reapply more finish. The idea is to fill the damaged area with new finish, but keep the surrounding area from building up. This is a lot easier to say then do, especially on a vertical surface like this appears.
Also if the finish is one of the harder polyurethanes, you'll have difficulty just with the repair approach, but for this, lets assume you can feather the area back and repair it. Do this with 120 grit at first to remove the bulk of the bad stuff and progress through 180 - 220 grit to remove scratches. Sand with the grain. With the old finish tapered back a few inches all around the damage, apply just enough finish to cover the raw wood. To this three or four times, letting the previous coat get very nearly dry before applying the next. This will bulk up some finish over the damage. After all this is well dry (at least 24 hours), block sand the area with the idea of removing any high spots on the damage, not removing additional material in the surrounding areas.
With high spots removed and any lows filled with more finish, you can move onto to finishing the whole area.
This is the "Cliff's" Notes" version and the actual the process could get quite involved, but most settle for considerably less. I'll let you decide when you're done.
Another approach would be a brass, bronze, plastic, stainless scuff plate over the area, knowing it will receive abrasion during the use of that knob. This certainly will be a much easier thing to affix.