@diver000: No, that's not the original name. There is no official full version of this song. "Not Tomorrow 1" is the official title from the soundtrack. The long versions are game rips where the titles were given by fans or the people who ripped them.
Very quiet, pretty song. Long ago I noted that this melody plays throughout many songs in the series, or at least very similar variations of it. "Promise" from Silent Hill 2 comes to mind, can't quite remember which others though. Too bad the full version isn't on the soundtrack CD.