This is dual to geometric realization.
But various other operations carry names similar to “totalization”. For instance a total chain complex is related under Dold-Kan correspondence to the diagonal of a bisimplicial set – see Eilenberg-Zilber theorem. As discussed at bisimplicial set, this is weakly homotopy equivalent to the operation that is often called and called the total simplicial set of a bisimplicial set.
Some kind of notes are in