Earl Wasserman informs us of the etymological debate over what the title--Epipsychidion--means:
C. D. Locock's etymology of the title, Epipsychidion, has been so widely accepted that it would take considerable temerity to discount it, were it not that James A. Notopoulos lends some support. Rejecting Buxton Forman's interpretation, "a little poem about a soul," Locock thought the title to be made up of the diminutive -idion and epipsyche, a neologism which he decided Shelley had "formed on the analogy of 'epicycle.'" Supported by Shelley's references in On Love to "a miniture...of our entire self" and "a soul within our soul" and, in the poem, to "this soul out of my soul" (238), he concluded that the title means "a little additional soul." This etymology has been so commonly accepted that it has even become a practice to speak of Shelley's theme of the "epipsyche" as though he had actually used that nonexistent term. But, as Notopoulos has pointed out, the word psychidion does occur in Lucian; and it has the sense merely of "little soul"--that is, the same animula, or little anima, to which Hadrian addressed his famous poem, the diminutive contributing only a sense of endearment. The prefix epi- need mean no more than "upon the subject of," and the full sense of the title is nothing more complex or subtle than "On the subject of the soul," which is what Emily represents. Although it is true that Shelley conceived of a miniature "soul within our soul" which is, according to On Love, "the ideal prototype of every thing excellent or lovely that we are capable of conceiving as belonging to the nature of man" and of which we seek the "antitype" in the world, there is no apparent reason for believing that the reference in the poem to the visionary ideal as "this soul out of my soul" has any direct bearing on the etymology of the title. But I believe both Notopoulos and Neville Rogers are correct in thinking Shelley also meant his title to be recognized as built on the model of epicedion, epicedion, and especially epithalamion" (418-19).
Wasserman, Earl. Shelley: A Critical Reading. Baltimore: Johns Hopkins P, 1971.