T. Eugene King, a 30-year veteran of First Security Corp., has been named president and chief executive officer of First Security Service Co., an FSC subsidiary.

The announcement was made by Spencer F. Eccles, chairman of chief executive officer of First Security Corp., who said King also was elected a member of the management committee of FSC. King succeeds Morgan J. Evans, who recently was elected chief financial officer of the corporation.King has served as executive vice president and manager of the information and services group of First Security Service Co. since 1983. He began his First Security career as a member of the Auditing Department in 1958 and later served in a variety of positions.

In 1973 he transferred to the service company in 1976 and was elected vice president and manager of systems and operations. He was promoted to senior vice president in 1981 and elected vice president in 1983.

In his new capacity, King will oversee First Security's retail banking and marketing group, the human resources group and data processing.