However, the idea of the additional ה' that was added to אברם is the Higher Letter ה' of Hashem’s name. Hashem’s Name has four letters: י-ה-ו-ה. These four letters correspond to four levels of Atzilus: י' to Chochma-Wisdom; the first ה', also known as the Higher Letter ה', to Bina-Understanding; ו' to Ze’eir Anpin-the Emotive Attributes; and the second letter ה', also known as the Lower Letter ה', to Malchus-Kingship. Adding the letter ה' to אברם means connecting him to the level of Binah, the first letter ה' of Hashem’s Name.
The Zohar (III 178a) says regarding the verse (Bamidbar 18:23) “The Levi works hard [to reveal] Him,” “Him” refers to the level of “Atik-Transcendent Pleasure.”
As explained elsewhere, the Levi in the Bais Hamikdash served Hashem through song and prayer (in contrast to the Kohen who served Hashem in action and quietly). In prayer, one contemplates on the greatness of Hashem so as to reveal their love of Him. This contemplation is through the soul power of Bina-Understanding. Atik-Transcendant corresponds to the transcendent level of the soul power of Pleasure, such as the pleasure felt when a concept is fully grasped; or in this context, the pleasure of connecting to Hashem on a deeper level after a contemplation of His greatness that is fully grasped.
For the revelation of “Atik-Transcendent Pleasure” is specifically in Bina, and not in Chochma.