I have never encountered anything more technical than words like "tube," "launcher," or "rack" in decades of reading nerdy military sci-fi including Battletech where those sorts of missile racks are absurdly common and both the authors and fans are weirdo military nerds.

Edit: looking at descriptions of rocket artillery vehicles like that on wikipedia I'm not running into anything more technical than "launcher," "launch system," or "multiple rocket launcher," with the older style of non-enclosed ones being mostly referred to as "launchers," "rails," or "launch rails," and if ever there was a place for weird nerds to flex their niche technical knowledge surely that would be it.