What are damages called that exceed compensation necessary to make the plaintiff whole?

The correct term for damages that exceed compensation necessary to make the plaintiff whole is punitive damages. Punitive damages are designed not just to compensate the injured party but also to punish the wrongdoer and deter similar conduct in the future. They are typically awarded when the defendant's actions are found to be particularly egregious or intentional, reflecting a desire to hold the defendant accountable beyond mere compensation for losses suffered.

Compensatory damages, on the other hand, are intended to cover the actual losses suffered by the plaintiff and restore them to the position they would have been in if the injury had not occurred. Nominal damages are a small amount awarded when a legal wrong has occurred but no actual harm can be proven, and liquidated damages refer to a pre-agreed amount stated in contracts for breach of that contract. Each of these has distinct purposes and outcomes in the context of legal proceedings, but only punitive damages serve the dual role of punishment and deterrence, which aligns with the criteria set in the question.