This paper is concerned with the Gromov–Hausdorff stability of global attractors for the 3D Navier–Stokes equations with damping under variations of the domain, which describes the complexity of the dynamics of the motion of a fluid flow. The Gromov–Hausdorff stability accounts for the Gromov–Hausdorff distance between two global attractors which may lie in disjoint phase spaces, as well as the stability of global attractors under perturbations of the domain. The same phase space cannot be used for the convergence via the Gromov–Hausdorff distance, which can be overcome, following Lee et al.(2020), by introducing a Banach space defined on a variable domain without “pull-backing” the perturbed system onto the original domain.