I'm Nobody! Who are you?
Are you - Nobody - too?
Then there's a pair of us!
Don't tell! they'd advertise - you know!

How dreary - to be - Somebody!
How public - like a Frog -
To tell one's name - the livelong June -
To an admiring Bog!

Meaning - Dickinson exclaims that she's a nobody and she's actually excited about it. She's meeting someone else. She exclaims her identity as “nobody” to that person, and asks the person, “Who are you?”. Then, in line two, she asks in a hopeful voice, “Are you- Nobody- too?” She seems to be hoping to have met another person who is also “nobody”.

In line three, she exclaims, “Then there’s a pair of us!”. She is clearly excited to have met another person who claims to be nobody. The speaker then admonishes her hearer not to tell anyone about the two of them each being “nobody”, exclaiming, “They’d advertise- you know!”. This reveals that she is clearly afraid of being found out. She enjoyed having no fame and no recognition, and she feared that if someone found out that she loved being “nobody” they would advertise her and make into into “somebody” and she dreaded that.

She believes that public life is dreary and cramped. It is like the life of a frog which tells its name all the time to the boggy ground where it lives. The speaker clarifies that it is dreary and dull to be Somebody. These Somebodies are public figures and later on they are compared to the frogs who just croak to the admiring bog. These public figures do not even try to say anything of significance; they just “tell one’s name,” that is, their own name so as to make themselves seem important figure. The “admiring Bog” is the group of people who permit the public figures to think that they are important and are praised. But the frog is not known outside the marshy bog.