Is the zombie asking for brains? Demanding? It seems like a compulsion that they can't control, but is it an exclamation? A declaration of intent? How would you classify it?
This seems to be holophrasis, a whole series of ideas in a single word, for example "howdy" for "how do you do" or "dead!?" to ask if the person laying in front of you has expired and your fear and revulsion at the fact. Depending on how "Braaains" is delivered it could a declaration of intend, a plea for sustenance, a statement of confusion. It all has to do with intent and delivery. There have been many iterations of zombies through out literature and cinema. If you are asking about what motivates zombies that may be more appropriate elsewhere.