Hi, I have looked into the place-name Qesem and see that its usual interpretation as a Hebrew word is "diviniation", as in casting objects that are interpreting as both meaningful and inspired by supernatural means.
The cave itself was only discovered in 2000 when road construction collapsed its hidden roof, so there is very little chance of a direct continuity relating to the function of the cave before its abandonment some 200 kya. That said I believe in site perpetuation - the idea that the role of a site or location can be carried forward unconsciously by the inhabitants of a place. Thus there has to be an importance in the name.
It would be my suggestion to look into the root of the word beyond Hebrew, in say East Semitic Akkadian, or in West Semitic Phoenician, Canaanite, or Carthaginian. This might provide even even closer idea of its root.