Point defects in altermagnets can create phases absent in the pristine host by selectively breaking crystal symmetries. Combining symmetry analysis, first-principles calculations, and Hamiltonian modeling, we identify how point impurities modify the altermagnetic phase. Using the pristine d- wave altermagnetic monolayer V2Se2O as a testbed, we identify three distinct classes of impurities: those that preserve spin-momentum locking, those that induce a hybrid-parity state associated with Edelstein spin conversion, and those that produce a metallic ferrimagnetic state with an anomalous Hall effect. We further discuss the robustness of two-dimensional altermagnets against point impurities. Results for other two-dimensional systems, such as Mn4N2 and 2H-FeBr3, reveal the same symmetry-based control across distinct lattices and parent spin harmonics, establishing defect geometry as a general route for engineering spin textures and transport properties.