I'm nobody! Who are you?
Nobody/Somebody reversal
Dickinson flips the usual value system—being 'nobody' is the desirable state, being 'somebody' is what you want to avoid.
Conspiracy of nobodies
The dash creates urgency—this is a secret alliance. 'Banish' suggests the somebodies have real power to exclude.
Frog metaphor
Frogs make noise to attract mates—their croaking is self-promotion. The 'admiring bog' is the frog's natural audience, not sophisticated listeners.