The local density of states of Mn-Mn pairs in GaAs is mapped with cross-sectional scanning tunneling microscopy and compared with theoretical calculations based on envelope-function and tight-binding models. These measurements and calculations show that the crosslike shape of the Mn-acceptor wave function in GaAs persists even at very short Mn-Mn spatial separations. The resilience of the Mn-acceptor wave function to high doping levels suggests that ferromagnetism in GaMnAs is strongly influenced by impurity-band formation. The envelope-function and tight-binding models predict similarly anisotropic overlaps of the Mn wave functions for Mn-Mn pairs. This anisotropy implies differing Curie temperatures for Mn delta-doped layers grown on differently oriented substrates.