The February 2003 Kickshaws (03-54) defined self-synonymy as two synonyms - if any exist that are spelled the same but are unrelated etymologically. David Silverman in an earlier Kickshaws (74-108) stated that if two words are homographic (and homophonic) synonyms they must be the same word. This seemingly obvious dictum would be refuted by a self-synonym pair. They're the same but not same. David Morice compared this idea to a linguistic Mobius strip. Schizograms is another apt name for such split personalities, but that coinage I reserve for coincidental contronyms (part III), where it applies doubly.
Word Ways: Vol. 37
, Article 15.
Available at: https://digitalcommons.butler.edu/wordways/vol37/iss1/15