Working in the perturbative limit, we develop the first analytical model predicting the dynamical excitation of quasinormal modes during the plunge-merger-ringdown stages for generic orbits, including highly eccentric ones. We find that quasinormal modes travel on hyperboloidal slices in the minimal gauge, and their amplitudes behave as activation functions near the waveform peak. Once the stationary ringdown regime is reached, a superposition of an infinite tower of non-oscillatory, exponentially damped terms appears. These terms are due to the source redshift at the horizon and can potentially swamp the overtone contributions. Our prediction shows good agreement with a perturbative numerical solution of the binary merger, but correct modelling of the prompt response is needed to fully reproduce the merger stage. We hence conclude by presenting a closed form model for the prompt response in a Schwarzschild spacetime, valid for sources localised far from the black hole.