The electronic structure and magnetism of an individual Dy atom adsorbed on the MgO(001) substrate is investigated using a combination of the density functional theory with the Hubbard-I approximation to the Anderson impurity model. The divalent Dy²⁺ adatom in ⨍¹⁰ configuration is found. The calculated x-ray absorption and magnetic circular dichroism spectra are compared to the experimental data. Quantum tunneling between degenerate |J = 8.0, Jz = ±4.0⟩ states leads to the formation of a |J = 8.0, Jz = 0.0⟩ ground state with an in-plane orientation of the magnetic moment. It explains the absence of remanent magnetization in a Dy adatom on the top of the MgO(001) substrate. Our studies can provide a viable route for further investigation and prediction of the rare-earth single-atom magnets.