For better or worse, the Arrowverse seems to take names from the comics but change almost everything associated with the name. Invasion and Crisis on Earth-X bore almost no resemblance to their comic namesakes. Invasion was a major turning point in the lives of Snapper Carr and Mon-El in the comics; both characters debuted on the Supergirl series shortly before the crossover yet neither even appeared in it. There was no alien alliance, and I don't think they used the Metagene bomb did they? Crisis on Earth-X in the comics was about the JLA and JSA fighting Nazis controlled by an evil AI and was basically just done to introduce the Freedom Fighters. The show did evil twins of the superheroes which in the comics was Crisis on Earth-3.

I would expect the Arrowverse COIE would resemble the comics in name only. I mean the fact that they have the Monitor and Anti-Monitor at all is almost surprising.