From the introduction to the Scholia to Lykophron’s Alexandra by John Tzetzes or his brother Isaac:

“Comedy is named either because of the time of the revel (kôma), since it was developed near sleep; because of the neighborhoods which are in the narrow streets (kômais); because of the villages (kômais) in the open countries; or because it developed in the vales (kômais) and places of Dionysus. But tragedy takes its name from the tragos or truga which is new wine: since in early times they anointed their heads with the raw wine. Or, they call it tragedy because they stand in a square (tetragônôs); or it turns from trakhodia into tragodia because they take their laments from harsh songs. Satyr-play is named from the satyrs who invented it or from the farmers and poor men.

καὶ κωμωδία δὲ κλήθη ἢ ὅτι κατὰ τὸν καιρὸν τοῦ κώματος ἤτοι τοῦ ὕπνου εὑρέθη ἢ ὅτι ἐν ταῖς κώμαις τουτέστι ταῖς στενωπαῖς ἢ ὅτι ἐν ταῖς κώμαις τουτέστι τοῖς μεγίστοις χωρίοις ἢ ὅτι ἐν ταῖς κώμαις καὶ τόποις τοῦ Διονύσου εὑρέθη. ἡ δὲ τραγωδία  ἀπὸ τοῦ τράγον ἢ τρύγα λαμβάνειν τουτέστι *νέον* οἶνον ἢ ἀπὸ τοῦ τρύγα χρίεσθαι τὰ πρόσωπα αὐτῶν κατ’ ἀρχάς· ἢ ὅτι τετραγώνως ἵσταντο, τετραγωδία ἐκλήθη ἢ ἀπὸ τοῦ τραχείας ὠδὰς ἔχειν τοὺς θρήνους τραχωδία καὶ τραγωδία. ἡ σατυρικὴ δὲ ἀπὸ τῶν σατύρων ἐκλήθη τῶν εὑρόντων αὐτὴν ἤτοι γεωργῶν καὶ εὐτελῶν ἀνθρώπων.

As in the case of dithyramb, this seems largely summarized from a contemporary dictionary, as in:

Etymologicum Magnum, s.v. tragodia:

“Tragedy: This is the dramatic performance of heroic lives and stories. It is called tragoidia because the prize that was given to the song was a goat [tragos têi oidê]. The song was thus the tragoidia. Or, those who won the competition took truga [“ripe grapes; or new wine”] as a prize. The ancients used to call new wine truga. Or, it is called this because the chorus had a four-sided shape [tetragônon]. Or because the choruses were composed of satyrs whom they used to call ‘goats’ [tragous] because they resembled them either because of their hairy bodies or because of their sexual zeal. For the animal was like that. Or tragedy is from the lees of wine [trugos]. This name has something in common with comedy, so the names of each type of poetry should be distinguished.

There was one prize for the latter, which is the truks [“new wine, lees”]. Later, tragedy had a common name [for the two?]. But the latter was named comedy since they used to perform them in the revels during the festivals for Dionysus and Demeter. This name came from “reveling” [kômazein] which is the song at the revel. This was developed at the time near sleep. Or it is the song of villagers [komêtai]. For larger rustic settlements are called kômai. Some farmers who were harmed by the citizens of Athens departed near the time of sleep. And those who lived near the roads used to refer to these wrongs which they suffered periphrastically. Thus, someone waits there and performs these deeds and others; as a results, there was to the injustice.

Τραγωιδία: ῎Εστι βίων τε καὶ λόγων ἡρωϊκῶν μίμησις. Κέκληται δὲ τραγῳδία, ὅτι τράγος τῇ ᾠδῇ ἆθλον ἐτίθετο· ᾠδὴ γὰρ ἡ τραγῳδία. ῍Η ὅτι τρύγα ἆθλον ἐλάμβανον οἱ νικῶντες· τρύγα γὰρ ἐκάλουν οἱ παλαιοὶ τὸν νέον οἶνον. ῍Η ὅτι τετράγωνον εἶχον οἱ χοροὶ σχῆμα· ἢ ὅτι τὰ πολλὰ οἱ χοροὶ ἐκ σατύρων συνίσταντο· οὓς ἐκάλουν τράγους, σκώπτοντες, ἢ διὰ τὴν τοῦ σώματος δασύτητα, ἢ διὰ τὴν περὶ τὰ ἀφροδίσια σπουδήν· τοιοῦτον γὰρ τὸ ζῷον. ῍Η ὅτι οἱ χορευταὶ τὰς κόμας ἀνέπλεκον, σχῆμα τράγων μιμούμενοι. ῍Η ἀπὸ τῆς τρυγὸς τρυγῳδία. ῏Ην δὲ τὸ ὄνομα τοῦτο κοινὸν καὶ πρὸς τὴν κωμῳδίαν· ἐπεὶ οὔπω διεκέκριτο τὰ τῆς ποιήσεως ἑκατέρας· ἀλλ’ εἰς αὐτὴν ἓν ἦν τὸ ἆθλον, ἡ τρύξ· ὕστερον δὲ τὸ μὲν κοινὸν ὄνομα ἔσχεν ἡ τραγῳδία· ἡ δὲ κωμῳδία ὠνόμασται, ἐπειδὴ πρότερον κατὰ κώμας ἔλεγον αὐτὰ ἐν ταῖς ἑορταῖς τοῦ Διονύσου καὶ τῆς Δήμητρος· ἢ παρὰ τὸ κωμάζειν, ἡ ἐπὶ τῷ κώματι ᾠδή· ἐπειδὴ ἐπὶ τὸν καιρὸν τοῦ ὕπνου τὴν ἀρχὴν ἐφευρέθη· ἢ ἡ τῶν κωμητῶν ᾠδή· κῶμαι γὰρ λέγονται οἱ μείζονες ἀγροί. Βλαπτόμενοι γάρ τινες γεωργοὶ παρὰ τῶν ἐν ᾿Αθήνῃσι πολιτῶν, κατῄεσαν περὶ τὸν καιρὸν τοῦ ὕπνου· καὶ περιϊόντες τὰς ἀγυιὰς, ἔλεγον ἀνωνυμὶ τὰς βλάβας ἃς ἔπασχον ὑπ’ αὐτῶν· οἷον, ἐνταῦθα μένει τὶς τὰ καὶ τὰ ποιῶν· καὶ ἐκ τούτου ἀνοχὴ τῶν ἀδικιῶν ἐγίνετο.