Maybe the Emmerians are referencing The Sky Crawlers : Innocent Aces. In that game, whoever is leading, their callsign became the squadron's name. Like when "Cougar" was leading, the squad is called Cougar Squadron. When Lynx became leader and changed into Cheetah, the squad name follows.

The Sky Crawler: Innocent Aces was released after AC6, not before.

Welp, got my estimation wron then. I thought with that kind of graphic it was released before AC6.

I guess it could help if we know whether there's a convention like this in the real world.

That isn't how it works in the real world at all. :P

You know what? I'm going to vote for Option 2 instead. Option 1 is a bit too inconsistent with callsigns convention, especially if you're going to call a squadron consisting of Sky Kid, Blue Max, and Red Baron "Sky Kid Squadron".

How is calling Sky Kid's team "Sky Kid Squadron" any diffrent from calling Avalanche's team "Avalanche Squadron"?

That's the thing. The unit members' callsigns are commonly related to something, like Windhover's squadron (Windhover, Lanner, Saker are falcons) and Hammerhead's squadron (Hammerhead, Hound Shark, Dusty Shark are sharks).

However, as you can see, one callsign is never above the others. Let's say that we have Apple, Orange, and Mango in a team. Should you call it Apple Team?

Well if the flight leader's callsign is Apple then I don't see why not. 

Also their callsigns are all related, they are all from the Namco game Sky Kid.

I believe this thread has reached its consensus, going with option one: calling the squadrons "X Squadron" where X is the callsign of the flight lead.