We study message identification over the noisy permutation channel. For discrete memoryless channels (DMCs), the number of identifiable messages grows doubly exponentially, and the maximum second-order exponent is same as the Shannon capacity of the DMC. We consider a $q$-ary noisy permutation channel where the transmitted vector is first permuted by a permutation chosen uniformly at random, and then passed through a DMC with strictly positive entries in its transition probability matrix $U$. In an earlier work, we showed that over $q$-ary noiseless permutation channel, $2^{c_n n^{q-1}}$ messages can be identified if $c_n\rightarrow 0$, and a strong converse holds for $2^{c_n n^{q-1}}$ messages if $c_n\rightarrow \infty$. For the $q$-ary noisy permutation channel, we show that message sizes growing as $2^{R_n \left( \frac{n}{\log n}\right)^{(r-1)/2}}$, where $r$ be the rank of $U$, are identifiable for any $R_n\rightarrow 0$. We also prove a strong converse result showing that for any sequence of identification codes with $$2^{\left(R_n n^{(q-1)/2}(\log n)^{1+\frac{(q-1)(q-2)}{2}}\right)},$$ messages, where $R_n \rightarrow \infty$, the sum of Type-I and Type-II error probabilities approaches at least $1$ as $n\rightarrow \infty$. Our converse proof uses the idea of channel resolvability. We propose a novel deterministic quantization scheme for quantization of a distribution over the set of all compositions/types by an $M$-type input distribution when the distortion is measured on the output distribution in total variation distance. This plays a key role in the converse proof. We have also studied identification with deterministic encoder and decoder, and proved tight achievability, weak converse, and strong converse.