Both quantum and classical behavior of single atomic spins on surfaces is determined by the local anisotropy of adatoms and their coupling to the immediate electronic environment, yet adatoms seldom reside on surfaces alone, and it is generally acknowledged that substrated-mediated interactions can couple single spins among each other impacting their magnetic behavior. Here we show that also magnetic anisotropy, which is usually considered to be a constant determined by the local crystal field, can be extremely sensitive to such interactions. By the example of Co dimers on Cu(001) and Pt(001) surfaces we highlight the intricate interplay of exchange coupling and magnetic anisotropy, providing a much sought possibility to tune the latter through deliberate adjustment of the adatoms\'separation. As a technologically relevant implication we demonstrate the impact of such emergent nonlocal anisotropy on the hysterectic properties of single-atom magnetization curves.