Actually, Grainger, I the grid nearest the cathode is the "control grid", or just "grid" in a triode. Next is the "screen grid", since it was said to "screen", or shield, the control grid from the plate. It is generally operated at a positive Voltage somewhat lower than the plate. The grid closest to the plate is the "suppressor grid", as you said, because it was said to "suppress" the secondary emissions that occur when the electrons hit the plate.
Keep in mind, a lot of the nomenclature is a product of its time!