It’s probably obvious from the title, but I’m specifically thinking of messages like
ProGamer64 [image of shotgun] L33tCamper
that appear in the bottom right corner when a kill happens, then fade away after a few seconds.
Is there a standard term for these messages or the list of them?
This is known as the killfeed.
This term has been widely used throughout many different multiplayer games, including old ones such as Quake, Counter-Strike, Starsiege’s Tribes, etc. For the etymology of the word the origin is unknown but it has likely started off with Quake/Quake II.
Some examples of killfeed from the games you have mentioned:
From Giant Bomb:
A standard in nearly all competitive online shooters, the Kill Feed is
the live on-screen update of the kills in an multiplayer game,
providing updates as to whom is killing whom, as well as other