[k_night]

We have one runner who is born rich, and famous.
One who likes to live above his station.
And the other just followed suit.
We are now known as "The suits".

[Chaos Monkey]

I have to confess that I have had the players in my game encounter an NPC crew called Dr. Teeth and the Electric Mayhem.

[Magnaric]

The team in the game I GM used to have a member who would get himself into serious trouble, and when talking his way out wouldn't work, he'd drop a grenade and run for it, shouting "Tweet tweet, motherf**kers!" at whoever might be pursuing.

That character has since died,  but the rest of the team call themselves the Road Runners in his honour.

[Sendaz]

Ran with a group for a brief time where all their characters were mimes save my own.

And yes, they did use silencers on their guns.

Lots of AR symbols and hand signs served pretty well for IC communication, some text would come across on the commlink though this was rare.

They didn't have a name of their own, but everyone else always referred to them as 'Those creepy f*****g mimes'

[CanRay]

The current crew I have playing Shadowrun ended up being called "Shadowrunner Ink", as that was the name of the tattoo studio that they operated out of, which is also a cover for an illegal trid-porn studio in the basement.

So far, they've expanded into the storefront beside them to hold their industrial chip burner and electrical generator, stolen two shipping containers that one of the PCs and a NPC live out of (stacked one on top of the other), gained a very old Japanese guy who refuses to speak English and does some very traditional styles of tattooing, extracted an IT worker from a call centre to do their online sales, kidnapped a dwarf DJ who is always blitzed out of his head on whatever he can find to do their Audio/Visual editing, and dealt with a Johnson who paid them in part with real fish.

[BetaCAV]

If all else fails, try http://fantasynamegenerators.com/squad-names.php

[firebug]

Recall there's the group "The Smoker's Club" in Shadowrun.  It's a wetwork group that both takes missions and gives them out.  Most recently lead by Riser, I believe it has some details in Hard Targets.

As Mirikon said though, group names are more likely to occur organically.  Especially if they're more street-level.