The self is usually referred to as the "atman," and the impersonal spirit as the "Brahman." Mircea Eliade, in his comprehensive study of Indian spiritual systems, writes about the Upanishads, one of the main spiritual texts: "The great discovery of the Upanishads was, of course, the systematic statement of the identity between the atman and the Brahman."
Pearl Beyond Price, pg. 15
"Atman" in Relation to Central Aspects of Essence
These three aspects, Space, Personal Essence and Essential Self, are the most central aspects of Essence. In the process of inner realization they, in some sense, replace the self-image, the separate individuality of ego and the sense of self of ego, respectively. Most traditional spiritual teachings can be grouped according to which of these three aspects they emphasize. Buddhism emphasizes Space, the prophetic tradition emphasizes the Personal Essence, and most of the Hindu systems emphasize the Essential Self, which they term the “atman.”
Pearl Beyond Price, pg. 316
Conceptualizations of Essence
Different spiritual traditions have given it different names: Christianity, Judaism, and Islam call it Spirit; Buddhism calls it Buddha nature; Taoism calls it the Tao; Hinduism calls it Atman or Brahman. The various traditions differ in how they conceptualize Essence and how much they emphasize it in their teaching, but Essence is always considered to be the most authentic, innate, and fundamental nature of who we are.
Spacecruiser Inquiry, pg. 169
Ego Identity is an Imitation of the Essential Identity
...this sense of identity, like all other sectors of the personality, is an imitation of a certain specific aspect of Essence. Ego identity is an imitation of the identity of Essence, the true self. The Hindus call it the Atman. The sense of identity of the personality exists because there is an unconscious memory of this true self. The personality's sense of identity develops through the loss of the true self. The child had it to start with, but its loss led to the development, through internalizations and identifications, of the ego sense of identity coalesced around a vague memory of the true identity. A self-representation is felt as relating to self because of this vague memory of self. This is the reason for the vagueness about identity in everybody's experience.