We currently have the following ruling authorities for Ethiopia:
People's Republic (1974-1991)
Federal Republic (1991-)
Neither are correct but getting the right names could be tricky. Archontology and World Statesmen give the following:
Ethiopia (1974-1987)
People’s Democratic Republic (1987-1991)
Ethiopia (1991-1995)
Federal Democratic Republic (1995-)
Both also say that Socialist Ethiopia was used officially between 1974 and 1987. Since we can't really just use Ethiopia, can I propose the following:
Socialist Republic (1974-1987)
People’s Democratic Republic (1987-1991)
Republic (1991-1995)
Federal Democratic Republic (1995-)
It's not perfect but is there a better solution?