Nanami normally has a dazed expression which gives her a sleepy demeanor, but she concentrates hard when she plays games. She often helps Hajime Hinata during school trials and provides important points. Nanami can also be stern when she tells people to do things and becomes a lot more lively when discussing games. She enjoys any kind of video game, even if she thinks they're terrible - with the exception of dating sims, the only genre she is bad at.
Major Spoiler
Nanami is actually revealed to be an AI created by Alter Ego to be a mole for the Future Foundation. She is the culprit of Chapter 5, where she is tricked into accidentally killing Komaeda.
Her being an AI is actually hinted at early on during the story. Her personal quirks such as her superhuman ability to concentrate and analyze, ability to sleep while standing, her lack of knowledge about the outside world and her long pauses before speaking.
During the events of Chapter 6, she fuses with Hinata and they break Junko's arguments.
In Zetsubou-hen, it is revealed that the AI Nanami was actually based on an actual student who attended Hope's Peak Academy along with the rest of the 77th class. She was originally an actual person in the real world, and an actual classmate of the Ultimates; in fact, she was unanimously elected class representative.
She was murdered by Junko Enoshima in episode 10 of Zetsubou-hen. Junko forced her to go through a dungeon filled with deadly traps before finally executing her when she reaches the goal. Nanami's death, which was filmed by Junko, is what she uses in order to drive the rest of the class into becoming the Remnants of Despair.
