Summary of the Explanation 

God Was before He created.
Before He created, ‘All That Is’ Was God.
God in Himself is perfect in unity.
In perfect unity there is no other.

Mind is the capability to experience being.
If there is no activity of mind there can be no awareness.
In a condition of being where there was only One, and that One was perfect in unity, there can have been no activity of mind.
Therefore when ‘All That Is’ was God, there was in Him no activity of mind.
Therefore when ‘All That Is’ was God, He was not aware.

To become aware of Himself required first that God become aware of other.

All that is not God is His creation.
Therefore God’s own Creation is the other of which He first became aware.

Therefore the first awareness in God was His first awareness of the beginning of His
Creation.
Therefore the entirety of the first awareness in God was His awareness of the condition of His creation in the beginning.
Therefore the entirety of the first awareness in God was His experience of being in relation only to that which had no form.
Therefore the articulation in God of His first awareness of the beginning of His creation was that ‘There Is’.

There Is, Therefore I AM.

Therefore ‘I AM’ was the articulation in God of the first experience He had of His Personal being.
The articulation in God of the experience He has of His Personal being must be identical to the articulation in Him of the knowledge He has of His Personal being.
Therefore ‘I AM’ is the articulation in God of the knowledge He has of His Personal being.

Personal identity is designated by means of a name.
The more knowledge of the one named that is articulated in their name, the more completely and specifically does it designate their personal identity.
Therefore the articulation of the knowledge God has of His Personal being is His perfect name.

‘I AM’ is the articulation in God of the knowledge He has of His Personal being.
Therefore ‘I AM’ is the perfect name of God.

Thus is I AM the name of God.