Drawing on:
History of Constellation and Star Names
In Greek astronomy the stars within the constellation figures were usually not given individual names. (There are only a few individual star names from Greece. The most prominent stars in the sky were usually nameless in Greek civilization. If there was a system of Greek star names then it has not come down to us and also would appear unknown to Ptolemy.)
List of proper names of stars – Wikipedia
From the Wikipedia page, clearly the only prolific namers of stars were the Arabs and the Chinese.
EDIT: I am adding data from Κατηγορία:Αντικείμενα Bayer – Βικιπαίδεια and Κατηγορία:Αστέρες ανά φασματικό τύπο – Βικιπαίδεια from the Greek Wikipedia. Additions are asterisked. As it turns out, several Latin names are translations of Classical Greek names.
In this catalogue, Ancient names are in boldface. The provenance of unbolded “traditional” Greek names is not always clear from the sources, but I am assuming they are post-Classical.
- θ¹ Eridani: (Arabic) Acamar. “The Greek-Persian astronomer Chrysococca [Georgios Chrysokokkes: Γεώργιος Χρυσοκόκκης – Βικιπαίδεια] called it Aulax in Greek, meaning the Furrow” Αὖλαξ.
- *α Tauri: (Arabic) Aldebaran. Greek name was (descriptive) “south eye of Taurus”; Ptolemy called it “bright star of the Hyades”; Modern Greek name is Lampadias Λαμπαδίας.
- α Scorpii: Antares Ἀντάρης
- α Boötis: Arcturus Ἀρκτοῦρος (already in Homer)
- ι Carinae: Aspidiske Ἀσπιδίσκη (per Iota Carinae – Wikipedia, Greek translation of Arabic Turais)
- ξ Puppis: Asmidiske †Ἀσμιδίσκη (Xi Puppis – Wikipedia: “a misplacement and mistransliteration of Aspidiske, the traditional name of ι Carinae; hence the name Asmidiske for Xi Puppis is not currently IAU-approved”)
- *α Orionis: (Arabic) Betelgeuse. Georgios Chrysokokkes called it Ōmon Didymōn Ὦμον Διδύμων “Shoulder of Gemini”
- α Carinae: Canopus Κάνωπος
- *α Aurigae: (Latin) Capella. Greek Aix Αἶξ (Aratus), Olenia Aix Ὠλενία Αἶξ (cf. Ovid: Olenium Astrum), Amaltheia Ἀμάλθεια. Capella “goat” is a translation of Aix; Amaltheia was the goat that brought up Zeus.
- *α Geminorum: (Latin) Castōr. Presumably also Greek Kastōr Κάστωρ. Also in “late Greek antiquity” Apollo Ἀπόλλων.
- α Canum Venaticorum: (Latin) Cor Caroli, Asterion Ἀστερίων
- β Canum Venaticorum: Asterion Ἀστερίων, Chara Χαρά
- This one is messy. Hevelius created the constellation, and named the Northern Dog Asterion and the Southern Dog Chara. β CVn is now named Chara, and α CVn Cor Caroli. Antonín Bečvář assigned the names Asterion to β CVn and Chara to α CVn.
- *α Ursae Minor: Polaris. Ancient name: Cynosure Κυνόσουρα (according to Greek Wikipedia, referred in antiquity only to the entire constellation), Phoinikē Φοινίκη.
- *β Leonis: (Arabic) Denebola. Ancient Greek Alkaia Ἀλκαία “lion tail” (also the origin of Denebola: ðanab al-asad).
- α Comae Berenices A: Diadem Διάδημα
- *ζ Aurigae: (Latin) Haedus. Hipparchus, Ptolemy: Eriphos Ἔριφος “kid goat” = Haedus. If Greek Wikipedia’s Protē Eriphos Πρώτη Ἔριφος “first kid goat” is classical, then η Aurigae: Haedus II would be Hetera or Deutera Eriphos Ἑτέρα/Δευτέρα Ἔριφος, “other/second kid goat”
- ζ Hydrae: Hydrobius Ὑδρόβιος (not official, not mentioned in Zeta Hydrae – Wikipedia)
- β Herculis: Kornephoros Κορ[υ]νηφόρος (properly in Ancient Greek korynēphoros)
- ζ Puppis: Naos †Ναός (Zeta Puppis – Wikipedia: intended to be Naus Ναῦς “ship”, over-Hellenised)
- β Geminorum: Pollux. Presumably also Greek Polydeukēs Πολυδεύκης. Possibly also Heracles Ἡρακλῆς, which was still used in Renaissance.
- *η Geminorum: Propus Πρόπους (in Hipparchus and Ptolemy)
- α Canis Minoris: Procyon Προκύων (in Aratus)
- *α Leonis: (Latin) Regulus. Ancient Greek Basiliskos astēr Βασιλισκὸς Ἀστήρ “royal star”. (Regulus means “little king”); Kardia Leontos Καρδία Λέοντος (? Ancient) corresponding to Latin Cor Leonis and Arabic Al Qalb al Asad.
- *β Orionis: (Arabic) Rigel. Georgios Chrysokokkes called it Pous Didymōn Ποῦς Διδύμων “Foot of Gemini”
- α Canis Majoris: Sirius Σείριος (already in Homer)
- α Virginis: (Latin) Spica (in Aratus: Stachys Στάχυς)
- ω Sagittarii: Terebellum (Terebellum (astronomy) – Wikipedia: originally Tetrapleuron Τετράπλευρον “quadrangle”, an asterism of four stars identified by Ptolemy, of which ω Sgr is the brightest)
- *α Lyrae: (Arabic) Vega. Greek Lyra Λύρα, after the constellation.
- ε Virginis: (Latin) Vindemiatrix (in Aratus: Protrygater Προτρυγετήρ, of which Vindemiatrix is the Latin translation)
- Pleiades:
- η Tauri : Alcyone Ἀλκυόνη
- 21 Tauri: Asterope Ἀστερόπη
- 27 Tauri: Atlas Ἄτλας
- 16 Tauri: Celaeno Κελαινώ
- 17 Tauri: Electra Ἠλέκτρα
- 20 Tauri: Maia Μαῖα
- 23 Tauri: Merope Μερόπη
- 28 Tauri: Pleione Πλειόνη
- 19 Tauri: Taygeta Ταϋγέτη