Zeros identity is a really big part of the story of this game and it is almost impossible to not find it out through the normal progression unless you play without volume and subtitles. You can enter it early, but it will cause you to get to the end of the game before you really know what is going on. I would really suggest you just play through the game naturally and wait until you progress to the point where you actually get it otherwise you will completely ruin the game's story.
If you don't want to wait or maybe you missed the piece of dialog where you should have heard it, highlight the black bar of text here to see what Zeros name is in Zero Escape Zero Time Dilemma.
Zeros Real Name = DELTA