Students

Izuku: Izzy

Bakugou: Suki

Denki: Pika

Iida: Zoom Zoom

Kirishima: kiri

Shoto: Icy Hot

Pro Heroes

All Might: Sweet boy, angel (He will love it) 

Aizawa: Zawa or Honey (this man needs affection asap)

Pres Mic: Boom or Zashi

Endeavor: Flame or Enji 

Villians

Dabi: Sparks 

Shiggiraki: Shiggy

Overhaul: Kai (his name, he doesn't care for nicknames) 

Kurogiri: Gi

Toga: Baby girl or knives 

Twice: Cutie or halvsies