There isn't really a nick name for Kim because Kim is the nickname for Kimberley.But a nick name can be anything that's suites the person and there habits it doesn't have do be from there 1st name either.
Some nicknames for kim is kimmy,k,kool kim, and kimmith.
Kim Sherrell goes by @kim.
Kim Sasabone goes by Lion Kim.
Kim Clijsters goes by Killing Kim, and Kim Kong.
for really imaginative people kambo is cute for like kailey, kallie, callie, or even katie
Kim Sanches goes by Kimi.
Kim Kanner goes by Shakira.
Kim Kahana goes by The General.
Dewey Kim goes by Dewey.
Emmeline Kim goes by Em.
Saerom Kim goes by Rommy.
Zo Kim goes by Zanshiro.