Apollo
Names & Epithets
Ἀγρέτεω (Agreteo) - either "the Assembler" or "the Hunter"[1]. As "the Assembler", perhaps related to the gathering of Zagreus' limbs. As "the Hunter", perhaps related to Orion. Survives in a single inscription from a temple to Apollo Phanaios[2].
Ἐλελεύς (Eleleus) - "the Shouter"[3], shared with Dionysus. From ἐλελεῦ, a Bacchic shout of revelry. Macrobius cites Euripides, Empedocles, and Plato using this epithet for Apollo as the Sun, giving its etymology as coming from "movement" (ἐλίττεσθαι) because of the Sun's course, or from "mass/collect" (συναλισθέντος / ἀναλισθεὶς) because it is a large collected mass of fire[4].
Φαναῖος (Phanaios) - from φαίνειν, a verb meaning "to reveal" or "to bring to light". There was a prominent Temple to Apollo Phanaios constructed at Phanai on Chios, modern day Kato Phana. This temple was dedicated in the 9th century BCE at the site where Leto learned would give birth to Apollo on Delos. This site and epithet are perhaps the historical origins of Phanes.
Φανεός (Phaneos) - "coming new (φαίνεται νέος) to our eyes" because the Sun rises anew every day[5].
Φάνης (Phanes) - "because he gives light (φαίνειν)"[5:1]. Phanes is a primordial Orphic deity often syncretized with various other Gods.