Etymologicum Magnum 256.6 s.v. ‘Dexion’ = T 69 Radt

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oὕτως ὠνομάσθη Σοφοκλῆς ὑπὸ Ἀθηναίων μετὰ τὴν τελευτήν. φασὶν ὅτι Ἀθηναῖοι τελευτήσαντι Σοφοκλεῖ βουλόμενοι τιμὰς αὐτῶι περιποιῆσαι ἡρώϊον αὐτῶι κατασκευάσαντες ὠνόμασαν αὐτὸν Δεξίωνα, ἀπὸ τῆς τοῦ Ἀσκληπιοῦ δέξεως. καὶ γὰρ ὑπεδέξατο τὸν θεὸν ἐν τῆι αὐτοῦ οἰκίαι καὶ βωμὸν ἱδρύσατο· ἐκ τῆς αἰτίας οὖν ταύτης Δεξίων ἐκλήθη.

Sophocles was given this name by the Athenians after his death. They say that the Athenians, wishing to procure honours for Sophocles after he had died, prepared a heroion for him and called him Dexion (the Receiver), after his reception (dexis) of Asclepius. Indeed, he received (dechomai) the god in his own home and set up an altar for him. For this reason, therefore, he was called Dexion.

Relevant guides Sophocles