Photius, Lexicon mu44 Theodoridis, not only gives this headword in nominative singular ("island of the blessed"; likewise already Hesychius mu110) rather than dative plural but also, more importantly, provides a route of understanding into what would otherwise be a baffling entry. The source cited is not Parmenides, the pre-Socratic philosopher (pi 675) but "Armendas", that is, the C5 BCE Boiotian historian Armenidas (FGrH 378 F5).
By the time A. wrote, the Theban acropolis surely bore its familiar name, the Kadmeia (see kappa 15). One must therefore wonder whether it had ever truly had any other name -- especially the strange one claimed here. The Islands (plural) of the Blessed were supposed to be the home of the happy dead in the far west: see generally OCD(4) p.747. Jacoby ap. FGrH 378 F5 inconclusively pursues possible mythological and high-poetic links between this and Thebes. Latte on Hesychius s.v. has a simpler solution: a misunderstood joke in Attic comedy (Comica adespota fr. 386 K.-A.).