Is the "verbal culture" of StormWorld essentially English, like in Forgotten Realms and Eberron? Or are there different cultures with different languages, like in Greyhawk or more especially, Mystara. The name of the race should be closely tied to whatever culture they originally derived from, unless, after 2,000 years, they have had sufficient time to evolve their own language and culture, in which case anything goes. And each culture/race in your world might have a different name for them, depending on their perspective toward the race. Elves, for example, might believe them to be an abomination, while dwarves might beleive them to be the chosen of the gods, if they are apt to use magical technologies. Maybe the dwarves even believe that "good" dwarven souls are implanted in newly-created warforged. Thus, the elves and the dwarves would ahve very different names for the race, in addition to the name the race has for themselves.
How does the race reproduce in your world? Are they dependent upon high-level mages to grow their numebers, or has something more "natural" developed (maybe a "sharing of the parts" whereby three or more of the creatures each add a bit of themselves to a new "youngling").
All these things will help determine how the race views itself, and thus what it calls itself, as well as what other races call it.
That said, I'd had a similar mechanistic race (metal, not wood based, and far more gear-based) from a science-fantasy setting, in which they were known as Mekhanikas. That might work if they view their existence from a mechanistic point of view, and if other races understand what that means...
If viewed as a form of golem, perhaps something further Hebrew sounding based on "golem", such as Golemim, or Gulim... maybe Mekhulim?
Further, if the world's "verbal culture" is English other names might include Gearz (form based), Druj (function based, if servitors), Kritani ("created"), or Uidjet (from "widgit," sounds good especially if they like wearing kilts and wielding claymores). Foreign sounding names would include Zahnrad (german for "gear," literally "tooth-wheel") and Mequan (vaguely French).