I am putting my 3 years of ancient greek and latin to use trying to deciper the Amphrous names, these are simple me having fun and theorizing, I don't work for Hoyo, this was just fun.
Okay so, Phainon in greek is "Φαινων", which is a participle form of the verb "φαινω" (faino), the verb means to bring to light, and thus the participle means bringing to light. So Phainon (Φαινων) means bringing to light.
Next up is Mydeimos, spelt "Μυδειμος" in greek, which is derived of "μυ" and "δειμος". "μυ" is a rewriting of μι’ which is a shortend version of μια and means one. "δειμος" is one of the greek words for fear, so Mydeimos (Μυδειμος) means one fear.
Aglaea (Αγλαεα in greek) is more simpler, being a different spelling of the word "αγλαια" meaning splendour, beauty or magnificence.
Anaxagoras is also simple, spelt Αναξαγορας in greek, and is named after a famous philosopher. Other than that, αναξ is also a greek word for lord or master and γοργας (the closest to goras i could find) meaning fear or terrifying, thus αναξ γοργας means lord fear or alternatively "lord of fear/master of fear."
Hyacine, Ὑασινε in greek, is from what I can conclude named after ὑακινθος (in greek)/hyacinthus (in latin), which is either the flower, hyacinth, or Apollo's lover, Hyacinthus, who he turned into said flower.
Castorice is one that made me laugh at first, because the latin word castor and the greek kαστωρ both mean beaver, castoris or καστορος then meaning beaver's. With further reading I think she's named a lesser known greek god, and not beavers. Castor plus the latin suffix -trix, later -ice in english, to make the name feminine. Castor and his twin brother Pollux are patrons of sailors.
And lastly (I chose to only do the characters we've met in game, I might add to this as the story progresses) is the one that made me sad, Tribios, Τριβιος in greek, created by adding the greek prefix τρι-, meaning three or three times, to βιος meaning life, thus Τριβιος means three life or life three times or three times life.
Followed by Tribbie, τριβιε, which honestly I think is just meant as a nickname, βιε is just a different form of the word βιος, so Tribbie and Tribios mean the same.
Trianne, Τριανε, has two options; either τρι + αν, αν here being a particle of emphasis, so "three!". Or τριαν, from τριας, which means three or triad.
And last is Trinnon, Τρινον, whose name made me the saddest, it can either be comprised of the prefix τρι- and the greek word νοον, from νους, meaning heart or soul, so three times heart/soul. Or the again the greek prefix τρι- and the latin non, meaning not, thus her name meaning not three.
I am now sad, and you all must suffer with the knowledge I now have. I am not sorry.