Why is Big Brother called Big Brother?
Big Brother is called Big Brother because the name combines two characteristics that the Party deems important for their continued control. On the one hand, he's big, indicating that he's strong and powerful and will therefore protect the people of Oceania as well as crushing its enemies. On the other hand, he's a brother, implying that he's someone you can love and trust, someone to whom you owe loyalty, just like a family member.
It's far from clear if Big Brother actually exists. When Winston Smith comes right out and asks O'Brien if he exists, O'Brien replies “Of course he exists. The Party exists. Big Brother is the embodiment of the Party.” Pretty clear, one would have thought. But then O'Brien muddies the water somewhat by denying that Big Brother could ever die. This would appear to suggest that Big Brother is more of a myth than a reality, a fake persona constructed by the Party to provide a focus of loyalty among the people of Oceania.
Whether Big Brother exists or not, there's no doubt that his name is well-chosen for the purpose that he serves. Big Brother's bigness is meant to emphasize the fact that he's strong, powerful, a fearless leader prepared to protect his people from all threats internal and external while crushing his enemies. The bigness of Big Brother also gives him a sense of ubiquity, as reflected in the notorious slogan “Big Brother is watching you”. The implication is that Big Brother is so big that he sees everything, and so no one should dare to do anything that might be considered vaguely subversive.
At the same time, Big Brother is not just a powerful, remote figure meant to instill fear in those deemed by the Party to be enemies of the state. He's also, as the name implies, a brother, like a member of the family. The word “brother” has connotations of love, loyalty, and respect. A brother is traditionally someone to whom we can turn in times of trouble.
And that's precisely the impression that the Party wishes to convey. The powers-that-be don't simply want people to obey Big Brother; they want them to love him. It's always much easier for a totalitarian regime to command the allegiance of its subjects through a mixture of love and fear, rather than through fear alone. And this is where the name of Big Brother, with its connotations of fear and love, comes into its own.