  We study one-dimensional Kitaev chain driven by the anisotropy parameter,
$J_{-}= t/\tau_Q$, in the presence of weak Gaussian noise in the parameter
$J_{+}$. The system is prepared in the ground state of the Hamiltonian at the
initial time $t\rightarrow -\infty$. The defect density and the residual energy
at the end of the drive protocol reveals anti-Kibble Zurek (AKZ) behavior which
deviates from the earlier reported linear in quench time dependence for the
defect density. The entropy density at the end of the protocol is found to
exhibit the signature of the AKZ behavior. In the context of the Kitaev chain,
the two-point spin correlators are short ranged. The hidden topological order
across the quantum phase transition point is probed via the non-local string
order parameters. The two-point Majorana correlator and the hidden string
correlator calculated in the final decohered state at the end of the noisy
drive protocol is consistent with the AKZ picture. We have analyzed the kink
statistics in the dual spin space, the first three cumulants at the end of the
noisy drive also exhibit the AKZ scaling behavior for slower sweeps similar to
the defect density. The kink distribution function is well approximated with
the normal distribution with non-universal noise dependent mean and variance.
