c, D, E can be eliminated. Can't decide between A or B. Not sure which one GMAT like but in general we say "The finance Minister Pranav Mukherji"....so would have opted for A.

A The author Herman Melville and the poet Walt Whitman are icons
B Herman Melville the author and Walt Whitman the poet are icons

C The author named Herman Melville and the poet named Walt Whitman are great icons
Extra great.

D The author, Herman Melville, and the poet, Walt Whitman, are icons
and the poet can modify either herman or Walt.

E Herman Melville, the author, and Walt Whitman, the poet, had been icons
had is wrong...they are still icons....as the original sentence says.

e] Incorrect. Had been should not be used. The authors are still icons

d] Whenever we use comma, it gives us extra information and so the information between commas is unrestrictive.. meaning even if you remove it, the sentence will make sense.
Since we are being very specific about the author and the poet, the usage of commas is incorrect.

c] Redundant word "named"

b] awkward structure. The way it is used, it should have commas i.e. Herman Melville, the author, and Walt Whitman, the poet, are icons

Option left is A