Based on the provided source material, there is no information available regarding a city named Umeki in the Kagoshima region of Japan. The name Umeki is identified exclusively as a Japanese surname.
Individuals with the surname Umeki include notable figures such as Kento Umeki and Tsubasa Umeki, who are both Japanese footballers, as well as Mami Umeki, a Japanese judoka. Additionally, Miyoshi Umeki is a Japanese-American singer and actress.