From here, under “Subject: Re: call sign” (an interesting article here based on these emails, about nuke-lobbing from propeller planes in the early Cold War):
So, when did they come along?
IIRC, they’ve been around since radio in the plane. My bud, who’s a Marine pilot, got his call sign in flight school. (He graduated around 1986, around the time when the movie came out).
It seems that nicknames were more prevalent decades ago. I can’t think of anyone I know with a nickname except for my mom’s husband Turk (short for “Turkka”). I remember watching a movie where a white-haired kid was called “Snow”, but that was a long time ago. Leavit to Beaver had “Lumpy”, but that was in the 1960s (or 1950s?). But nowadays, at least here in Los Hideous, I never hear nicknames. (Wait – I do hear some among some ethnic groups; but no one I know.)
Back in the 1930s and 1940s you had pilots with names like “Smilin’ Jack” (a comic strip) and James B. “Earthquake McGoon” McGovern. IIRC RAF Spitfire ace Douglas Bader used “Dogsbody” on the radio. And of course, there was Gregory “Pappy” Boyington.
My guess is that pilots used their everyday nicknames as their “handles” dating back to WWI. Esprit de corps and all of that. I think that pilots “always” had nicknames. If the quote in the OP is correct, then I’d guess that sometime in the 1970s a pilot “had” to have a nickname to be part of the “club” and that Top Gun just made the practice better known.