When listing to the song "The Only Exception" by Paramore (see YouTube), there's a screeching sound when changing chords, which I find quite unpleasant.
Question: Is there a name for the screeching sound made when changing chords on a guitar?
The name for the noise you're hearing is "string noise". It is caused by the fingertips scraping across the round-wound strings of the instrument when the hand changes from one position to another.
"Fret noise" is the name used by Yamaha and others for that sound in synthesizers.
I think it's more often than not called "fret noise" which is sort of a misnomer since it does not actually have a lot to do with the frets (it would be rather strenuous if you did not even clear the frets while changing chords). Bona fide fret noise would be notes getting hammered on or single-string (or power chord) slides with pressure on so that you have sort of a sequential hammering-on or pulling-off of frets.
The more accurate term "string noise" (even though it can include twanging sounds) will likely be perfectly understandable to any player.