the war itself has been called the Genocide this far. I've been toying with the idea of calling it the Second War (as opposed to the quasi-mythical "First War", the one where the Deodrah, the proto-freespacers, overthrew their slavers and fled to space), but I think that Genocide works fine. It's what it has been called OOC, too.
The fall of the Lighthouse could be called, metaphorically, the Darkening, which could later be referred as the period of time that goes from the fall of the Lighthouse (and the disruption of the core of Polysentience) until the day in which Polysentience will return to 100% of its usual effectiveness, sometime in the near future.
I don't think that there should be a name for the Yamataian declaration: after all, it's a Yamatai matter and few 'spacers are likely to know, or to care. But since then, in news posts and alike, I've had the Freespacers rename Yamatai "The Fascist Empire of Yamatai", both out of spite and because, learning more about Yamatai, they realized that it's an "empire" in the real sense of the word, that is, a nation where a single person detains power.
This concept, obviously, is so ridiculously alien to the anarchic, communist, collectivist Freespacers that it's almost as if the United States of America today were ruled with absolute power by the god-king Xerxes as portrayed by Frank Miller's 300 and corresponding film, complete with gold and opulence, harem of freaks, merciless conquering and pillaging of Canada and Mexico, and war campaigns in Europe... to make a funny comparison.
We can make up other names as we go along. For example, if the proposal of a gathering point in Nep space is approved, that point could be known with some fancy name and Freespacers might leave there a shrine or some other kind of memorial.