They called it commonwealth in their own languages. Rzeczpospolita in Polish, Žečpospolita in Lithuanian. Both from Latin res publica, "public matter", which in turn might be familiar to you as the root for "republic", though often indeed translated as commonwealth in the past. The two constituent realms were the Korona Królestwa Polskiego, the Crown (lands) of the Kingdom of Poland, and Wielkie Księstwo Litewskie/Lietuvos Didžioji Kunigaikštystė, quite literally the Grand Duchy of Lithuania.

It was called "Rzecz(y)pospolita Obojga Narodów" - Republic of Both/Two Nations. (y) is pronounced but not written.