  In this article, we discuss the existence and asymptotically autonomous
robustness (AAR) (almost surely) of random attractors for 3D stochastic
globally modified Navier-Stokes equations (SGMNSE) on Poincar\'e domains (which
may be bounded or unbounded). Our aim is to investigate the existence and AAR
of random attractors for 3D SGMNSE when the time-dependent forcing converges to
a time-independent function under the perturbation of linear multiplicative
noise as well as additive noise. The main approach is to provide a way to
justify that, on some uniformly tempered universe, the usual pullback
asymptotic compactness of the solution operators is uniform across an infinite
time-interval $(-\infty,\tau]$. The backward uniform ``tail-smallness'' and
``flattening-property'' of the solutions over $(-\infty,\tau]$ have been
demonstrated to achieve this goal. To the best of our knowledge, this is the
first attempt to establish the existence as well as AAR of random attractors
for 3D SGMNSE on unbounded domains.
