I think it is from movie only but not so sure. In movie

From MCU wiki During the starting development of the initiative, the team's original name was meant to be named Protectors, until Fury decided to name it as Avengers, after Captain Marvel's former Air Force pilot call sign.

In comic

From wikipedia, in "The Coming of the Avengers" The Avengers 1 (Sep 1963) The first ever Avengers adventure was Loki trying to get Thor killed by Hulk. He tricked Hulk into destroying a railroad and then diverted a distress signal meant for Fantastic Four to Thor, hoping for a confrontation and demise of his brother by Hulk. However, this distress signal was also received by Ant-man, Wasp, and Ironman, who defeated Loki and resolved the matter. Ant-man at this point realized they worked together and named the group as Avengers

In the comics, Danver's callsign was "Cheeseburger", so we were this close to Nick Fury recruiting people for The Cheeseburger Initiative...

This is indeed a movie invention; the images from the original comic in the accepted answer say it all, but for what it may worth, here is an excerpt from Avengers Assemble: An Oral History of Earth's Mightiest Heroes by Brian Michael Bendis (Marvel, 2012), which draws directly from the canon of the original comics, and not the movies:

Doctor Henry Pym: Credit where credit is due. The name Avengers came from Janet.

Janet Van Dyne: I said that. That was me. I threw it out there. Everyone was spitballing and I said "the Avengers" and everybody grabbed it. So yeah.

Where of course Henry Pym and Janet Van Dyne are the original Ant-Man and the Wasp, respectively, both founding members of the (comics original) Avengers.

It isn't consistent with the comics...

... not the stories that take place within the prime, Earth-616 continuity, at least. In that continuity, the Avengers team with Thor, Hulk, Iron Man, etc wasn't actually the first Avengers team, canonically speaking.

A later story established that the first Avengers team was formed in 1959 (Marvel Universe-time), before Carol Danvers was even born, never mind in the Air Force. (We know she was in the Air Force prior to the formation of the modern Avengers, since she and Ben Grimm, AKA the Thing, flew on a mission together when he was still a pilot himself, before either the Fantastic Four or the modern Avengers had formed.)

Nick Fury (the original version) was involved with the formation of the 1959 Avengers, however, he didn't come up with the name; he was told what the name would be by his superiors, and instructed to recruit and lead the team. The dialogue indicates that the orders, and possibly the name of the team itself, came directly from the US President (which would've been President Eisenhower, assuming Marvel Universe history aligns with real world history in that regard).

New Avengers Vol 2 #9

Avengers 1959 Vol 1 #5

Also, as noted in Ross Thompson's answer, when the comicbook version of Carol was in the Air Force, her call sign was apparently "Cheeseburger", not "Avenger".

Ms. Marvel Vol 2 #32