When you name your group "The Avengers" presumably you are avenging something (or someone) right?
In the recent The Avengers film, they don't embrace the "Avengers" name until
Agent Coulson's death.
So, that's what they're avenging. Although Stark's line "If we can't protect the Earth, you can be damn sure we'll avenge it," makes for a nice snippet of dialogue for trailers, the spoiler is what the plot of the film has them avenging.
In the MCU we now have a clear reason for the name. In the 2019 movie Captain Marvel, we learn that
Nick Fury named his proposal for "The Avengers Initiative" on Carol Danvers' call sign, printed on her plane as Capt Carol "Avenger" Danvers
which he saw in a file photo of her plane when she'd been a test pilot for Pegasus. The link is very clear; the paper was titled "The Protectors Initiative" until Fury saw the photo, reconsidered, then went back and edited the document to reflect the Avengers name.
The name appears blanked out in this photo, which was available before the movie release, but the pilot's name would be printed where the white rectangle is:
presumably you are avenging something (or someone) right?
Yeah, and that's exactly why at the beginning the group has been named Avengers. Not Prevengers. Not Defenders. Not Guardians. Not The Deterrers, too (those are actually called The Annihilators, by the way).
They are called Avengers because the exact purpose of the group is to avenge. And avenge what, you ask? Well, whatever needs to be avenged, clearly!
The Avengers are a group of distinct superheroes each one minding their own business; they were founded as a team of heroes working on-call: they are not patrolling, defending or investigating something together. To quote the old Avenger motto, they team was established
to fight the foes no single super hero could withstand
Only when there is a wrong to avenge, and it's a wrong that cannot be fought by a single hero, the Avengers assemble.