I propose "can". Then, the Superheavy booster is its "kicker". Both lower-case.
I agree that this thing, a Falcon refitted with cans' Raptor engines, is a natural follow-on once the engine is flight-proven. But it will face very stiff competition from a whole new generation of rocket startups. It might not get common enough to need its own nickname.
Is "starship" not already generic enough?
i suspect once space travel is common and every day enough it will become mundane to talk about it and at that point an improper noun like ‘can’ will become commonplace. i figure this will happen 2 to 3 decades from now
It is anyway nothing at all like what we call a starship in any other context. It resembles a shuttle rather more than STS did.
It is unfortunate that we don't have a short name for "suppository", which it resembles more. I guess "bougie" could work.