1 In Burmese, Kai means strong or unbreakable. 2  In Chinese, Kai is a common name that can have one of several meanings, including triumphant (凱) 3  In Cornish, Kai means dog, and is often used as a dog name. 4  In Estonian, Kai is a female name meaning pier.  In Finnish, Kai is a common male name, Finnish form of Kaj.