When you complete the game and then select the 'New Game' option you will be able to select an alternate costume for Enoch. To unlock the other alternate costumes you must complete the corresponding tasks.
Unlock Dark Enoch (Enoch, transformed into a warrior of darkness by the Dark World): Complete Chapter 8 with an 'A' or better rank.
Unlock Old Armor A (Blue): Complete the game.
Unlock Old Armor B (Brown): Complete the game.
Unlock Rider: Complete Chapter 6 with an 'A' or better rank.
Unlock Special: Collect ALL Ishtar Bone Fragments from the Dark World portals. Wearing this costume will prevent you from taking damage but will not give you points for fighting or collecting items.