Investiture is what happens when a government official, a judge, or a head of state is formally put into office or promoted to a higher rank. The investiture of a king is an elaborate, lengthy ceremony.
The noun investiture is good for describing the process of naming a judge or a church bishop, for example, to office. Investitures tend to include ritual ceremony and the symbolic transfer of a position from one person to the next. In the US, Supreme Court justices are invested with the position — which literally means "clothed in the official robes of office." Both words stem from the Latin investire, "clothe in" or "cover."