His (or her!) modus operandi is actually pretty simple. Anybody can right-click a corporate logo for use as a Facebook profile picture, and then create a false account using a corporate-sounding name and a throwaway cell phone number. (Troublingly enough, spammers are known to do the same thing to impersonate private users, by right-clicking publicly available profile pictures.)
But this guy is the Lex Luthor of trolls, and his antagonism of complaining Target customers achieves the level of online performance art. The controversy into which he’s inserted himself is whether or not Target should have gender-specific sections for children’s toys.
Check out some samples of his pathos via this recent article at Adweek: