Symbolism, Imagery, Allegory
BIG BROTHER IS WATCHING YOU. Scared yet? Big Brother is the face of the Party, the leader behind the great power. The best part is that we never come to confirm his actual existence. He might not even be real. Maybe the Party just hired an intimidating-looking male model to make those posters. The face of the Party, Big Brother acts as reassurance and a trustworthy entity for many (his name is warm and fuzzywarm and fuzzy and easy to embrace). Yet, he is also your biggest enemy and threat – if you are one of the criminals (he is watching your every move).
So about his name. This is more irony. "Big Brother" should be a nice guy that, even if he gives you wedgies once in a while, still has your back on the playground. But since war is peace, freedom is slavery, and ignorance is strength, Big Brother is also a controlling and not remotely brotherly guy.