The story
Blend of K + Hamiltonian; apparently popularised by a jocular comment in the textbook Classical Mechanics by Herbert Goldstein (first published 1950). "It has been remarked in a jocular vein that if H stands for the Hamiltonian, K must stand for the Kamiltonian! Of course K is every bit as much a Hamiltonian as H, but the designation is occasionally a convenient substitute for the longer term "transformed Hamiltonian""
Etymology from Wiktionary, CC BY-SA 4.0.