pUShA connection
pUShan also had a caduceus-like rod in the shruti; and goat is the animal of pUShan; and is associated with the dog of agohya. (details).
Hermes is one of the yavana cognates of the Arya puShan. The homology here is split between Hermes & his son Pan. While Hermes is a cognate of H puShan, his name might also be a cognate of saramA the mother of the hell-dogs in the H tradition.
प॒थ एकः॑ पीपाय॒+++(←प्या वृद्धौ)+++ तस्क॑रो यथाँ
ए॒ष वे॑द निधी॒नाम् ॥One makes the paths prosperous, like a thief this one knows the sites of treasures.
This connection with paths & thieves is shared plainly with Hermes.
Wealth
Socrates: Is it not well to pray to the deities here before we go?
Phaedrus: Of course.
Socrates: O beloved Pan and all ye other Gods of this place, grant to me that I be made beautiful in my soul within, and that all external possessions be in harmony with my inner man,
May I consider the wise man rich; and may I have such wealth as only the self-restrained man can bear or endure.
Do we need anything more, Phaedrus? For me that prayer is enough.
Phaedrus: Let me also share in this prayer; for friends have all things in common
Pūṣā is associated with acquisition of wealth & particularly with recovery of lost wealth (naṣṭadravyaprāpti) (RV 6.54.7, 10) as well as making a stingy man’s heart soft (RV 6.53.3) & in general impelling a man towards the vedamantra (6.53.8). (yām pū̍ṣan brahma̱coda̍nī̱m…) - GA
All
Source: TW
A yavana sealing showing god Pan with a goat before the fire altar surrounded by the zodiacal belt. In the Greek tradition Socrates in this theological exposition associates Pan with “all” -> pan – a wordplay. He says: “Then Pan, who declares and always moves (ἀεὶ πολῶν) all…” This is reflected in the sealing as the zodiac.
Thus, the “all-ness” of Pan in the Socratic discourse has deep roots with a reflex in the vaidika ritual. Details
Hermes and Pan
In the H world the Ashvin-s, bhava & sharva, skanda& vishAkha are reflexs of the same old IE deities reintroduced by different Aryan streams that entered India. Just like that we hold that Hermes & Pan are to distinct introductions of same puShan-class deity by different streams of Greeks. Following the multiple introductions in both traditions the multiple layers are reconciled as distinct deities through reassignment of syncreticism.