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We study one-dimensional Kitaev chain driven by the anisotropy parameter, $J_{-}= t/τ_Q$, 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.