In Avengers: Infinity War when the Avengers lost and 50% started disintegrating, was there a name given to the event? The Event, The Disintegration, The Loss?
It's called the Decimation.
Marvel has been carefully avoiding exploring the consequences of the snap, so as not to spoil any plot details for Avengers 4. With the sole exception of one of the post-credits scenes of Ant-Man & the Wasp, none of the movies have been set in this period. The Marvel Television shows have dodged the snap - even Agents of S.H.I.E.L.D., whose fifth season was heavily influenced by Thanos' attack. This silence has come to an end, however with the publication of Brandon T. Snider's The Cosmic Quest Volume Two: Aftermath. A young adult book, it doesn't go into great detail about the horror of it all, settling for throwaway references to the chaos that ensued on a global scale. But, for the first time, it officially reveals the in-universe name for the event fans have long been calling the "Snappening."
To the Earth's surviving population, the moment when half the life on the planet crumbled to dust is known as "The Decimation."
I don't believe the "event" is specifically referred to by name but I'd suggest that it's probably called "The Vanishing".
Circumstantial evidence provided by the memorial in San Francisco visited by Scott Lang.
The lost people are called "The Vanished".
Alternatively, it seems general knowledge that Thanos was responsible for what happened and so it could be referred to a "Before Thanos" and "After Thanos"