Does the SATURDAY NIGHT LIVE cast have a Group-Name Now? (The Way They Used to Call Themselves "The Not-Ready-for-Primetime Players")

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That's what the SATURDAY NIGHT LIVE-cast called themselves when the show was just starting (and their show's title was just SATURDAY NIGHT, because there already WAS a SATURDAY NIGHT LIVE whose cast called themselves 'The Prime Time Players.') http://www.faqs.org/faqs/tv/sat-night-live/faq/ They dropped the designation in the fourth season, but did they pick another one up? I don't think they did, but I might have a few suggestions: The Nerd Table (as I've heard it's kind of the basis of their comedy---skits based on 'wouldn't it be weird'-ideas like nerds talk about among themselves), Drama Geeks, Parody Punks, The Sanctum Sarcasm (a geeky joke based on Doctor Strange's "Sanctum Sancorum" in the MCU). Any other suggestions? or do the SNaiLs (another suggestion) have a name they go by already?