Terminology to describe people who "awaken"

[Minyatur]

To me if we say that what makes us asleep is the veil, then being awake means to perceive yourself that went under a veil.

I would not equate being aware of the nature of reality with being awake. If you are dreaming and notice that there is gravity in your dream, you won't tell yourself that you were awake in the dream but instead aware of an aspect of the reality of the dream. To be considered awake in a dream, you need to remember in some way yourself from outside the dream.