The name itself came from the Trump administration, who used the first set of mystery illnesses to take potshots at Cuba. It stuck, unfortunately, but they’re up to over 200 cases, most of which have jack-all to do with Cuba.
As for “syndrome” - that’s generally used when we have a cluster of symptoms that appear to be somehow related (either same symptoms, or many symptoms that are temporally clustered) but for which no actual cause is described. This sort of plays havoc with the notion of “one thing,” because very often syndromes can actually be multiple concurrent diseases or other phenomena that are not intrinsically linked.
Basically, there’s too much noise to figure out what’s causing what, and there’s no clear explanation. What we do know for a fact is that a sampling of people who report symptoms have brain damage that was observed via MRI and reported in JAMA in 2019, so the symptoms are possibly rooted in physical brain trauma of some kind.
It is not, as some people say, a simple headache, or a hangover, or conversion disorder - there’s real observable brain damage under those symptoms.
I’m personally skeptical of the “directed energy weapon” thing, mostly because there really isn’t strong evidence for any cause right now. The microwave radiation thing is the best explanation right now, but just because scientists give their best explanation right now doesn’t mean that’s the explanation in which they place any real credence. I see that explanation as the “well, fuck it, this is the best I’ve got right now, and it’s stupid, but here it is.”
It reminds me of the time I non-ironically suggested “ghosts” when trying to suss out a persistent PCR contamination problem in the lab - because at some point, when there’s nothing reasonable left, you suggest wacked-out shit as a way to say “we need to do some serious exploration.” It turned out to be dust from ceiling tiles, which is basically the same thing as ghosts anyway, but the point is that sometimes scientists just shrug and give “fucked if I know” as an actual answer.
I come back to: the symptoms are real, so something happened, so the people with symptoms need treatment and the thing needs to be investigated as a real thing that actually happened.