What is the name of the political system ruled by nonelected council? Similar to corporate rule. I call it councilism, but looking for better name.
In the generalities, a political system ruled by a few persons is an oligarchy:
Oligarchy (from Greek ὀλιγαρχία (oligarkhía); from ὀλίγος (olígos), meaning 'few', and ἄρχω (arkho), meaning 'to rule or to command') is a form of power structure in which power rests with a small number of people.
After that, there are a number of specific categorization that can be applied to the group, depending on extenuating circumstances.