You can do it as long as you're not mocking Starbucks, because they're sensitive and delicate souls who'll
sue your pants off.
Actually, if you're worried, I think the better thing would to have a thinly-veiled but recognizable parody of the corporation/logo to mock or simply have your characters and narrative always refer to the actual corporation by the nickname alone.
"Arrrhbucks" and their nautically-themed/pirate logo, perhaps. 