Goku keeps his identity through all his Super Saiyan transformations, including Super Saiyan 3. This form requires the full extent of Goku's energy and has, at times, caused more harm to him than to his enemies.
After seven years of training in the Other World, Goku was the first to harness the power of Super Saiyan 3. The first time Goku achieved this transformation on Earth, his power caused earthquakes and tidal waves. The form was very difficult to control and eventually done away with once he learned the much more stable and effective Super Saiyan 4 in "Dragon Ball GT."