The extraction of "fingerprints" from human brain connectivity data has become a new frontier in neuroscience. However, the time scales of human brain identifiability are still largely unexplored. We here investigate the dynamics of brain fingerprints along two complementary axes: (i) What is the optimal time scale at which brain fingerprints integrate information and (ii) when best identification happens. Using dynamic identifiability, we show that the best identification emerges at longer time scales; however, short transient "bursts of identifiability," associated with neuronal activity, persist even when looking at shorter functional interactions. Furthermore, we report evidence that different parts of connectome fingerprints relate to different time scales, i.e., more visual-soma-tomotor at short temporal windows and more frontoparietal-DMN driven at increasing temporal windows. Last, different cognitive functions appear to be meta-analytically implicated in dynamic fingerprints across time scales. We hope that this investigation will advance our understanding of what makes our brains unique.