Update 2: Trailer available for viewing.
The Phantom Pain is indeed Metal Gear Solid V, Kojima Productions revealed at a keynote by Hideo Kojima at the Game Developers Conference this morning.
The Phantom Pain is an open-world game and together with Metal Gear Solid: Ground Zeroes, forms Metal Gear Solid V, Kojima Productions said. It appears that Ground Zeroes and The Phantom Pain are the same game.
The game starts out with Snake waking up after being in a coma for nine years and he has to escape the hospital he’s in. This sequence forms the game’s tutorial.
Update: Metal Gear Solid V (which is Ground Zeroes + The Phantom Pain) is in development for the Xbox 360 and PlayStation 3, but the game is currently running on PC.