Final Fantasy - NES, Released in US (as Final Fantasy)
Final Fantasy II - NES, Not Released in US
Final Fantasy III - NES, Not Released in US
Final Fantasy IV - SNES, Released in US (as Final Fantasy II)
Final Fantasy V - SNES, Not Released in US
Final Fantasy VI - SNES, Released in US (As Final Fantasy III)
The PSP remake of Final Fantasy II is the remake of a game that was never released in the US. The main characters are Firion, Guy, and Maria.
The game you are remembering is Final Fantasy IV (which was called Final Fantasy II for the SNES). The main characters are Cecil, Kain, and Rydia. There are a lot more but I can't remember them right now. This game was remade twice; once for the GameBoy Advance, and once for the Nintendo DS.
EDIT: Which is exactly what Timber said. I just wanted to elaborate a little more.
