The naming choices of powerful rulers encode millennia of cultural, political, and institutional influences. Consequently, the long-term onomastic dynamics within some of the most powerful dynasties cannot be explained by simple mechanisms such as frequency-dependent reinforcement or random name reuse. Here, we propose a minimal model that encapsulates these influences in a single highly stochastic variable, prestige, and assume that name selection is driven by the prestige accumulated by previous rulers bearing the same name within each dynasty. Using an extensive dataset spanning ten dynasties, we show that the model reproduces the pronounced inequalities in name frequencies, the long-term persistence of dominant names, and the abrupt rises in popularity observed in historical records. Our results suggest that the naming traditions of powerful rulers preserve institutional memory through reinforcement while remaining sensitive to rare historical events that can reshape the hierarchy of names across generations.