Neko usually does not wear underwear to school because she enjoys, or needs, the sense of danger it causes.
Neko was overweight at the time when she met Masamune Makabe for the first time. As such, he does not recognize her when they meet during high school, similar to Masamune's situation with Aki Adagaki.
Neko's favorite snack is ketchup, and she's used it before as to disguise her real bleeding as fake blood to not cause concern to Masamune.
She is also the first kiss of Masamune.