|A depiction of Echo (left) and Narcissus (right) story, as told by Ovid (8AD), by English painter John Waterhouse (1902); shown with annotation by Thims (2020), the supposed way Goethe perceived the story, as alluded to in his Elective Affinities. |
A 1902 depiction of Echo (left) and Narcissus (right) by English painter John Waterhouse, the synopsis of which, in Ovid's version of the myth, is: 
"Narcissus was the son of the river god Cephissus and the nymph Liriope. His parents were told that he would live to an old age if he did not look at himself. He rejected all the nymphs and women who fell in love with him. One of these was the nymph Echo, who was so upset by her rejection that she withdrew from life and wasted away until all that was left was a whisper. Her prayers were heard by the goddess Nemesis who caused Narcissus to fall in love with his own reflection. He continued to look at his reflection until he died."
The extrapolation of this, to Goethe’s Elective Affinities, is that Ovid’s myth tells the story of fate of Ottilie (Echo) and Edward (Narcissus), who both meet their ends by similar fates.
The first to have made a connection between the Narcissus myth and Elective Affinities seems to have been English Germanic literature scholar Frederick Stopp (1911-1979) and his 1959 article “A True Narcissus: Reflections on the Eduard-Ottilie relationship in Goethe’s Wahlverwandtschaften.” 
Others to explore connections between Ovid’s Narcissus myth and Goethe’s Elective Affinities, according to Stefani Engelstein (2008), were German philologist Waltraud Wietholter (1982) and American literary critic J. Hillis Miller (1992).  Miller, who cites neither Stopp nor Wietholter, may have been the first to pick out the "hidden anagram", as he calls it, in the names of the four main characters: 
"The name 'Echo' may even be present in the novel as a hidden anagram of the names of the four main characters: Edward, Charlotte, the Captain (der Hauptmann), and Ottilie."
Scottish biographer and German literature lecturer John Williams (1998) also discusses the hidden ECHO acronym anagram, along with several others. 
1. Williams, John R. (1998). The Life of Goethe (pgs. 233). Blackwell.
2. Stopp, Frederick J. (1959). “Ein Wahrer Narziss: Reflections on the Eduard-Ottilie relationship in Goethe’s Wahlverwandtschaften.” (pg. 62) Publications of the English Goethe Society.
3. (a) Engelstein, Stefani. (2008). Anxious Anatomy: the Conception of Human Form in Literary and Naturalistic Discourse (pg. 52-53; 259). SUNY Press.
(b) Wietholter, Waltraud. (1982). “Legends: The Mythology of Goethe's Elective Affinities” (“Legenden: Zur Mythologie von Goethes Wahlverwandtschaften.”) Deutsche Vierteljahrsschrift 56(1): 1-64.
4. (a) Miller, J. Hillis. (1992). Ariadne’s Thread: Story Lines (pgs. 205-206).Yale University Press.
(b) J. Hillis Miller – Wikipedia.
5. (a) Echo and Narcissus – Wikipedia.
(b) Thims, Libb. (2020). Human Chemical Thermodynamics — Chemical Thermodynamics Applied to the Humanities: Meaning, Morality, Purpose; Sociology, Economics, History, Philosophy, Government, Anthropology, Politics, Business, Jurisprudence; Religion, Relationships, Warfare, and Love (pdf). Publisher.
● Metamorphoses – Wikipedia.
● Echo (mythology) – Wikipedia.