For the Cu(100), Cu(110), and Cu(111) surfaces varying asymmetric line shapes are found for the atomic 3d⁸4s² multiplet two-hole final state binding energies reached in MVV Auger photoelectron coincidence spectroscopy. Higher asymmetry for Cu(111) and Cu(110) in comparison to Cu(100) is caused by reduced dynamic screening for Cu(111) and Cu(110) in contrast to free electron like Cu(100). This is a consequence of the surface projected band gaps in Cu(111) and Cu(110) not present in Cu(100). We describe the distinct tailing in the experimental line shapes of the three Cu surfaces with first principles calculations of layer-dependent two-hole binding energy shifts, depth-dependent intensity distribution and Doniach-Sunjic asymmetry parametrization. These fundamental insights into the surface-specific electronic structure can advance the understanding of structure-reactivity relationships in Copper-based surfaces and catalysts.