Who is his companion in the story?

The man Goodman Brown meets in the woods outside Salem that night, whom he had clearly had pre-arranged to meet, is described as:

...about fifty years old, apparently in the same rank of life as Goodman Brown, and bearing a considerable resemblance to him...they might have been taken for father and son.

We are told that he has a worldly air about him and that his staff

bore the likeness of a great black snake, so curiously wrought that it might almost be seen to twist and wriggle itself like a living serpent.

The serpent, of course, symbolizes the devil, and even Goodman Brown admits to himself that his is out there on a “present evil purpose.” It is often said that the devil has the power to assume a pleasing shape (just ask Hamlet), and so readers are to put the pieces together and determine that Satan has disguised himself as young Goodman Brown’s grandfather (as we will soon learn). The young man might be attempting self-denial, but he knows full well whom he is meeting with.
There are other clues to the dark nature of the companion. He says he came through Boston just 15 minutes ago—an impossibility. He also claims to have had dealings with Brown’s grandfather, which would make him much older than 50 as described, and to have influence over the souls of nearly everyone in Salem Village. The devil’s identity is corroborated by Goody Cloyse when she greets him in the woods:

"The devil!" screamed the pious old lady.
"Then Goody Cloyse knows her old friend?" observed the traveler, confronting her, and leaning on his writhing stick.
"Ah, forsooth, and is it your worship, indeed?" cried the good dame. "Yea, truly is it, and in the very image of my old gossip, Goodman Brown, the grandfather of the silly fellow that now is. But, would your worship believe it? My broomstick hath strangely disappeared, stolen, as I suspect, by that unhanged witch, Goody Cory."

Later at the meeting, which is actually a devil-worshiping ceremony in the parody of a church service, Brown’s companion takes the pulpit, gives a sermon in which he promises his followers that the earth

...shall be yours to penetrate, in every bosom, the deep mystery of sin, the fountain of all wicked arts, and which inexhaustibly supplies more evil impulses than human power—than my power at its utmost—can make manifest in deeds.

The Devil then inducts Goodman Brown’s wife Faith and another village member into their fold: "‘Welcome,’ repeated the fiend worshipers.”
By this point, even Goodman Brown cannot deny to himself the identity of his companion; there is no mistaking the devil himself.
http://www.articlemyriad.com/analysis-summary-young-goodman-brown/