  We study how time-dependent energy fluctuations impact the dynamical quantum
phase transitions (DQPTs) following a noisy ramped quench of the transverse
magnetic field in a quantum Ising chain. By numerically solving the stochastic
Schr\"odinger equation of the mode-decoupled fermionic Hamiltonian of the
problem, we identify two generic scenarios: Depending on the amplitude of the
noise and the rate of the ramp, the expected periodic sequence of noiseless
DQPTs may either be uniformly shifted in time or else replaced by a disarray of
closely spaced DQPTs. Guided by an exact noise master equation, we trace the
phenomenon to the interplay between noise-induced excitations which accumulate
during the quench and the near-adiabatic dynamics of the massive modes of the
system. Our analysis generalizes to any 1D fermionic two-band model subject to
a noisy quench.
