Hiya!!
I love your idea, but you have to be very careful to make sure it’s distinct, as Greek mythology gets a lot of traction. It could be interesting to use minor/less well known gods as well - I’ve suggested a couple of similar deities for each. Maybe consider the Titans? Or [name_m]Roman[/name_m] mythology as an alternative? It’s fundamentally the same, but less well known/used. [name_m]Roman[/name_m] versions of Posideon, [name_f]Athena[/name_f] and [name_f]Aphrodite[/name_f] are [name_u]Neptune[/name_u], [name_f]Minerva[/name_f] and [name_f]Venus[/name_f]. 
Demigod 1 - I love the idea of a character named ‘[name_u]Red[/name_u]’ being of [name_m]Poseidon[/name_m]!! Other water gods: Aegaeon; Amphitrite or Nerites (consorts of [name_m]Poseidon[/name_m]) [name_m]Oceanus[/name_m]; Triton.
Not a massive fan of [name_f]Crimson[/name_f] - it might be a bit to the point, and takes away from the blunt appeal of [name_u]Red[/name_u] as a nickname. [name_u]Red[/name_u]-related names include: [name_u]Flynn[/name_u]; [name_u]Ruby[/name_u]; [name_f]Poppy[/name_f]; [name_u]Auburn[/name_u]; [name_f]Ceara[/name_f]; [name_u]Rory[/name_u]/[name_f]Aurora[/name_f]; [name_f]Shona[/name_f].
[name_u]Flynn[/name_u] would be my favourite for her - but with Fray, [name_u]Ruby[/name_u] Fray or [name_f]Aurora[/name_f] ‘[name_u]Rory[/name_u]’ Fray sound good. 
Demigod 2 - (NOTE - I read your description and assumed he was male! I’ve chucked in some female names too just in case ahah.) I like him !! If you wanted it to be related to [name_f]Athena[/name_f] in some way, her symbols are mainly olives; spears; owls and snakes.
- [name_m]Oliver[/name_m]/[name_f]Olivia[/name_f] (the olive tree) - I really like '[name_f]Oly[/name_f]' as a nickname.
- [name_m]Tito[/name_m] or [name_m]Otis[/name_m] (greek words for owl were ‘tuto’ and ‘otos’)
- [name_m]Phineas[/name_m] - “[name_u]Finn[/name_u]” (means mouth of a serpent in Hebrew; is also a character in greek mythology.)
- [name_m]Drake[/name_m] (means dragon/serpent)
- Owl/[name_u]Bird[/name_u] names - [name_u]Shannon[/name_u], [name_f]Jenna[/name_f], Eerin
- [name_f]Linda[/name_f]/[name_f]Melinda[/name_f]/[name_f]Linnie[/name_f] (means serpent)
These names mean ‘peace’ - an interesting link, as olives are symbols of peace but [name_f]Athena[/name_f] is a goddess of war. Might go well if you’re carrying the ‘opposite’ theme of [name_u]Red[/name_u] and [name_m]Poseidon[/name_m].
- [name_u]Shiloh[/name_u], [name_m]Calum[/name_m] or [name_m]Jonah[/name_m]
- [name_f]Irene[/name_f], [name_f]Jemima[/name_f], [name_f]Shanti[/name_f], [name_f]Idra[/name_f]
Notable places where [name_f]Athena[/name_f] was worshiped include Lucera ([name_u]Luca[/name_u] or [name_m]Luke[/name_m]); and as a goddess of craft and weaving ‘Kaltz’ ([name_m]Kal[/name_m]) or ‘Teller’ (both meaning weaving) suit.
OTHER WAR/KNOWLEDGE DEITIES: [name_f]Alala[/name_f], Enyo, [name_u]Nike[/name_u], Kratos, Coeus, Metis, Prometheus
Demigod 3 - firstly, [name_f]Hera[/name_f] is notoriously monogamous in mythology - she has no demigod children, and unless you make it a very important story point, I would avoid having a character descended from [name_f]Hera[/name_f]. [name_f]Leah[/name_f] I really like, [name_f]Alaska[/name_f] not as much. I do really like her as a daughter of [name_f]Aphrodite[/name_f] - names related to beauty include - [name_f]Lana[/name_f]; [name_f]Ella[/name_f]/[name_f]Ellen[/name_f]; [name_f]Lily[/name_f]; [name_f]Adara[/name_f]; [name_f]Callie[/name_f] ([name_f]Calida[/name_f]; Callissa; [name_f]Callia[/name_f]); [name_f]Alina[/name_f]; [name_u]Keely[/name_u].
[name_f]Aphrodite[/name_f] is related to doves; roses; apples; hares and youth:
- [name_m]Melo[/name_m] (Greek for apple) - [name_f]Melonie[/name_f]/[name_f]Melanie[/name_f] - [name_f]Melina[/name_f]
- [name_f]Rosa[/name_f]; [name_f]Rose[/name_f]; [name_f]Roselyn[/name_f]; [name_f]Rosanna[/name_f]; [name_f]Roisin[/name_f]; [name_f]Rhonda[/name_f];
- Meaning Rabbit - [name_f]Lulu[/name_f]
- Meaning youth - [name_f]Lianna[/name_f]; [name_f]Juliet[/name_f]/[name_f]Juliette[/name_f].
My favourites would be [name_f]Callie[/name_f]; [name_u]Mel[/name_u] ([name_f]Melina[/name_f]/[name_f]Melonie[/name_f]) or [name_f]Lulu[/name_f].
OTHER GODS OF [name_u]LOVE[/name_u]/SEXUALITY: [name_m]Eros[/name_m]; Anteros; Potus; Himeros.
I really like the sound of your story! [name_f]Hope[/name_f] you enjoy it x