I'm going to fall into the non-cap version of kryptonite - it's a noun, like table, oxygen, dog, meteorite, earth(dirt).
It's not a proper noun (name) like George, Irving, Frank, Earth(planet).
The way I figure it Kryptonite is the trademarked version. While kryptonite is found in meteorites (either from Smallville or Addis Ababa)


Big Apricot Superman Movieverse
The World of Lois & Clark
Richard White to Lois Lane: Lois, Superman is afraid of you. What chance has Clark Kent got? - After the Storm