Single atom alloy (SAA) clusters formed by anchoring single atoms in small supported host clusters are emerging as catalysts with high performance. In this work, density functional theory (DFT) calculations and ab‐initio molecular dynamics (AIMD) simulations are performed to study the stability and the structure evolution of γ‐alumina‐supported platinum/copper SAA clusters of sub‐nanometer size in hydrogen environment. Due to the strong dynamic nature of both Cu cluster and anchored Pt single atom and their evolving interaction with the support, different isomers with different geometric and energetic properties are predicted. Extensive sampling through AIMD simulations reveals strong effect of hydrogen on the location of Pt single atom and strong variation of the cluster shape, evolving from 3D to concave and planar shapes wetting the alumina support. Interfacial site location of Pt single atom is found to be hydrogen coverage dependent. When the hydrogen coverage increases, the Pt single atom located preferentially at the interfacial site is pulled up by hydrogen atoms toward the upper surface Cu layers. The interaction of Pt/Cu cluster with alumina is predicted to decrease with increasing hydrogen coverage. Finally, electronic structure analysis reveals dramatic effect of hydrogen on the metallic nature of the catalysts.