As an example, my current group ran into a rival 'runner team just last week. They've also negotiated for jobs while some of these other ones were sniffing around similar job leads and will likely square off against one at some point, or, rather, have a tense moment where they're both breaking into the same place at the same time.
Notes are in another room, but off the top of my head:
Team Seven
The best-of-the-best, a SHadowrunning team famous for being professioanl and efficient. They're just about to go corporate and hook up with a corp full-time as Company Men. When they do, that'll leave an opening for the other teams to all move up a step.
Behind the 8-Ball
The name started as a joke, but now they're stuck with it. Pretty much the opposite of Team Seven, they're sloppy, unprofessional, and have miserable luck. Several of their team have broken off and joined other groups, leaving them a shell with neither decker nor magical support. They're down to taking the worst jobs and trying to get by.
The Steel Vixens
An All-Female team, put together for looks more than talent. They record *everythng* and have their own reality show, mostly taking fake jobs set up by their producers but sometimes taking real, if soft, missions. They sometimes scoop members from other teams, if they think that they can fill a marketing niche.Don't think of them as shallow bimbos ... the senior members are pretty ruthless business types. They sell a product, and defend it violently.
KABOOM!!!
What it says on the tin. They're demolitions and distractions experts, hired for monkeywrenching and tailchasing almost exclusively. If you want quiet, then you don't want KABOOM!!! on your side.
The Merry Men
'Hooding-focused 'runners. They do a fair level of pro-bono work, but mostly they work for poor pay to combat things like polluters or racists. Not as skilled or well-paid as many other teams, but beloved and sheltered by the community. "Made Marian" is their leader, a mafioso's daughter who's wealthy enough to put the team up in general.
Blue Screen
A team of all-deckers and combat deckers. Needless to say, they're data specialists.