We show that charge doping can induce transitions between three distinct adsorbate phases in hydrogenated and fluorinated graphene. By combining ab initio, approximate density functional theory and tight-binding calculations we identify a transition from islands of C8H2 and C8F2 to random adsorbate distributions around a doping level of +/- 0.05 e/C atom. Furthermore, in situations with random adsorbate coverage, charge doping is shown to trigger a sublattice ordering transition when the doping level exceeds the adsorbate concentration. Rehybridization and lattice distortion energies make graphene, which is covalently functionalized from one side only, most susceptible to these two kinds of phase transitions. The energy gains associated with the clustering and ordering transitions can exceed room temperature thermal energies.