The most commonly used Portuguese name for grandmother is avó. Variations are avozinha, vovó or just vo.
Interestingly, both grandmothers and grandfathers are referred to as avo, but the pronunciation is different. Avô for a grandfather is pronounced "a-voh," with the variant vovô being pronounced "vo-voh." Avó for a grandmother is pronounced "a-vaw," with the variation vovó being pronounced "vo-vaw."