Terminology for worst-case N-complexity on $O(1)$ insert after amortisation
The case, when the operation performs the worst, is commonly called the worst case.

The common name for the optimization you mentioned is de-amortization.

To denote the fact that operations take $O(1)$ on average, you may say that the time complexity of a single operation is amortized $O(1)$.

As far as I know, amortized complexity analysis was first introduced by Robert Tarjan in his “Amortized Computational Complexity”, where you can look up more usages of the term.