In my games a long standing team typically didn't name themselves. It's an organic process that they eventualy end up getting on on themselves to shape their reps better.
One of the longest standing teams I GMed we're basically "just some runers" for a very long time, but a run against CATco that went down in a rather spectacular way. They were caught on camera at great distance zipcording between two skyscrapers (it wasn't part of the plan, they'd actualy screwed up and were cornered by security in a conference room) followed by stealing a chopper on the roof and eventually remotely crashing it in the bay in front of more TV cameras (that WAS intentional, they called the press with an anonymous tip to get the authorities and CATco off the scent for a bit). They followed that by gettign caught on TV cameras AGAIN two weeks later doing a fast decend from another building during a Azzie press party for some product release while a banner slamming the Azzies environmental record unfurrled above them.
Their exploits, needless to say, became something of a street legend and their reps got added to with every retelling. Eventually a Johnson said to them with, "so you're those urban legends I keep hearing about." A few jobs later someone refered to them as "So you're Urban legends?" Since it was already pinned on them, they adopted it as a "team name" as it was already being used and recognized.
That's how it typically goes in games I GM or play in. The name itself is organically grown based on what they do and (as a GM) they are offered a number of choices and opportunities for those ogranic names to appeal to them and for them to adopt it. After that, it's how they use it that determines if it sticks or they keep it.
