The word "identity" occurs only a couple of times in "Song of Myself," but it is easily the central theme of this vast epic. Whitman sees his identity split into at least three components: his everyday personality, the more inner "self" or "Me Myself," and the universal "Soul." He was attracted to the American Transcendentalist idea of the "Oversoul," or the soul that is somehow part of or connected to all other souls in the world. For him, there is no such thing as "private experience." He experiences the pains and pleasure of all other people in the world, and even animals and inanimate natural phenomena, because he "identifies" with them. That is, his innermost identity is connected to all things in the world.
When Whitman celebrates "himself," he refers to Transcendentalism's great soul that connects all things.
The poem has two primary speakers, Whitman and the "Me Myself." His soul does not and cannot speak for itself.