Currently only one kitten of the Kitten Catastrophe Crew has been named: Tabby (Cat Rocky).
Each member of the KCC resembles a member of the original PAW Patrol (Chase, Marshall, Rubble, Rocky, Skye, and Zuma) and has a similar role/equipment (Cat Skye is the team's air support and Cat Zuma acts as the team's diver). The Kittens act as a foil for the member they represent (for example Cat Rocky litters and breaks things and Cat Chase breaks the law and is mischievous). Additionally, Mayor Humdinger acts leader of the KCC and serves as the human counterpart to PAW Patrol's leader, Ryder.
The KCC was apparently created by Mayor Humdinger as a counter to the PAW Patrol in response to his and his town repeatedly losing competitions between Foggy Bottom and Adventure Bay (which he and his town had previously won and/or been undefeated in) due to the intervention of Ryder and PAW Patrol. As a result, its primary goal is to aid Mayor Humdinger (and by extension their hometown of Foggy Bottom) in winning various completions between Mayor Goodway and/or Town of Adventure Bay that she represents.
Despite them being the PAW Patrol enemies and all the trouble they cause, Rubble considers the kittens to be cute. However, Chase apparently has a negative opinion of them, as he points out they have a Secret Lair in "Pup-Fu!". However Chase's negative opinion of the Catastrophe Crew may be due to his role as a Police-Pup sworn to uphold the law (and the fact they where guilty of the crime of theft in "Pup-Fu!").
Due to Chase's kitten allergies, he often sneezes when he comes across the Kitten's scent, which the PAW Patrol have come to consider to be a tell-tale sign the Catastrophe Crew is causing trouble. The kittens have also been known to use Chase's allergy against him which may contribute to his dislike of them.
Unlike the Pups, the Kittens aren't as dedicated to their role as the Pups are at saving the day, as they have been known to sometimes ignore or choose not to follow Mayor Humdinger's orders, preferring to play or eat (such as when they decided to eat candy instead of making balloon bouquets for Friendship Day as Mayor Humdinger had ordered them to in "Pups Save Friendship Day"). However this may be due to their mischievous nature and given the fact that cats generally are not as obedient as dogs.