An identifying code in a graph \( G \) is a set \( D \) of vertices such that the closed neighborhood of each vertex of the graph has a nonempty, distinct intersection with \( D \). The minimum cardinality of an identifying code is denoted \( \gamma^{ID}(G) \). Building upon recent results of Gravier, Moncel, and Semri, we show for \( n \leq m \) that \( \gamma^{ID} (K_n \Box K_m) = \max\{2m – n, m + \lfloor n/2 \rfloor\} \). Furthermore, we improve upon the bounds for \( \gamma^{ID}(G \Box K_m) \) and explore the specific case when \( G \) is the Cartesian product of multiple cliques.