I'm of the opinion that you don't ever get to choose your street name. The Street does, meaning your friends, your employers and even your enemies. You might decide you want to have "Skullcrusher" as your handle, but after a few bad moves running from the 'Star, you get to be known as 'Trippy'. You might like the name "Whisper". But after some great one-skill shots with your sniper rifle, now the Street is calling you 'Reaper'.
Technically how it would work is that you'd start with a version of whatever name you presented to the team -- or just a title based on what you do (like "Sam" ,"Spells", "Rigs", et cetera -- always one syllable, easy to say), then when you get your first point of Street Cred, you get a Street Name to go with it. If it's something you don't like? Then it's on you to change it, and that means doing things to make people think differently of you. So instead of using that sniper rifle, you get to sneak around and maybe pull off a few garrotings, and Trippy better start hoping his dice roll better.
This takes a number of runs to do -- I'd say double your current Street Cred -- and when you're done, you lose half your Street Cred, rounded up, minimum of one. After all, you're not 'Trippy' anymore...
