The Hunger Games return with such a sequel twist that you can't believe writer Suzanne Collins didn't think of film when writing. Catching Fire builds up with all types of subversive messaging which is interesting but also brings into relief the limitations of the genre and film.
Each kaiju is given a name when it first enters the breach. The names always alternate between a Japanese one and an English one.
The six kaiju shown in detailed fight scenes in the movie are (in order of appearance) Knifehead, Leatherback, Otachi, Raiju, Scunner, and Slattern. The kaiju in the Tokyo flashback is Onibaba.
The four primary jaegers in the movie are named Gipsy Danger (USA), Cherno Alpha (Russia), Striker Eureka (Australia), and Crimson Typhoon (China). The jaeger shown in the Tokyo flashback is Coyote Tango.