Keep in mind that the definition of personification is giving human qualities to something that is not human. As a result, you cannot "personify" a person. The question here might better be looked at as a question of whether Rabbit Angstrom is characterized as a rabbit or is his nickname a metaphor for something else?
I would argue that the author is doing both. Think about two things: first, characterization includes all the techniques an author uses to define a character's personality, including direct description, and indirect techniques such as the character's appearance, thoughts, dialogue, actions, and the reactions of others to him. Second, what are common qualities of a rabbit that could be used metaphorically or symbolically here? Rabbits are known for rapid reproduction, quickness (physically), and sometimes for wit or smarts (like Bugs Bunny). They are often adored as lovable pets, but also hunted for food and sport.
I encourage you to consider the above techiques of characterization and the symbolic/metaphoric qualities of rabbits in order to personally discern what Updike may be saying through his main character's nickname.