I know this is more than 5 each so don't feel like you have to do all of them, I just struggle to narrow this down to anything smaller.
Don't hesitate to switch some of the middle names around, I'm still playing around with some of them myself.
Lux Cassidy or Lux Athena
Arizona Kate or Arizona Marie
Eden Aurora or Eden Annabelle
Luna Artemis or Luna Penelope
Cassandra Monroe or Cassandra Melody
Milo Alistair or Milo Poseidon
Jonas Maverick or Jonas Aries
Tate Aries or Tate Jupiter
No worries on the long lists
Jessa Quinn - I like how it sounds as a combo, but individually I'm not a fan of either name on a girl. Since my name's Jenna, I've never really been a fan of close-but-different names like Gemma and Jessa for some reason. Also, I grew up with two male Quinns, so it's just hard for me to see the name on a girl. Not a bad combo though.
Piper Keeley - Piper is one of those names I might like on someone else's kid, but at the same time I have trouble seeing it aging. Keeley is nice, I go back and forth on whether I like it or not. Overall, the combo has a good flow. It just feels really young to me, like I can't see it on an adult.
Lux Cassidy or Lux Athena - I'm iffy on Lux but I could see liking it a little bit. Lux Cassidy sounds a little clunkier to me just because of the hard X and C sounds, but Lux Athena has a great flow, and I love the meanings of both names together - light, and the goddess of wisdom. I definitely really like Lux Athena as a combo!
Arizona Kate or Arizona Marie - I like the use of a classic middle with such an uncommon first name. Arizona is really interesting and spunky, it reminds me of Alaska, which is sort of a GP of mine. As individual names, I like Kate better than Marie, but I think that for flow purposes here I would go with Arizona Marie - it feels a little abrupt to have a one-syllable middle after a longer first name.
Daphne Shay - There's something about Daphne that I've never really liked, sorry. Shay is an interesting one, I'm not sure if I like it better on a girl or a boy. This combo has good flow though.
Penelope Brooke - I love Penelope (especially with nicknames Penny or Nellie) but I'm iffy on Brooke. It feels like a millenial-generation name to me, and I'm not sure I like it as a middle here.
Lola Temperance - Ah, yes! Someone else who likes long, classic-but-uncommon names in the middle spot! I could take or leave Lola (it feels a bit nickname-y) but I could see liking it after meeting a little girl with the name. Temperance is really nice with it.
Juno Antigone - I like Juno, as I have an affinity for Jun- names on girls in general (unfortunately, my dad just got a dog with this name so I have trouble picturing it on a human now. But it's still a great name!). Antigone I'm not so sure about, both because of the tragic story attached to the name and because the spelling brings to mind two relatively negative concepts, 'anti' and 'gone.' As a combo, it's okay, but I think there might be a little too much N in there.
Eden Aurora or Eden Annabelle - I love love LOVE Eden as a first for girls! It's been on and off my list forever. I definitely prefer Eden Annabelle, it just has a really lovely sound and flow overall. Eden Aurora is nice too, I'm just not much of a fan of Aurora as a name.
Luna Artemis or Luna Penelope - Luna is a GP of mine, so I like it and would love to see it on someone else's kid. I like the use of Artemis as a middle in general (I'm a big fan of Greek mythology), I just can't decide whether I like that both names are related to the moon or if it's too much. Luna Penelope is really really pretty, but I would love to see Penelope as a first.
Cassandra Monroe or Cassandra Melody - Cassandra is one of those names that I go back and forth on. I like Cas names on both girls and boys, but I feel like the -sandra ending ages it a little. With that said, it is a really nice name. Monroe is just one of those names I can't get myself to like, sorry. But I love Melody in the middle spot, and Cassandra Melody has a really nice flow.
Julian Anchor - Julian is one of those names that I really love but just wouldn't use myself, so I love hearing it on others' lists. Anchor is interesting... I've never heard it, but it's close to the popular Archer and on trend with word names, so I can totally see it working. I really like this combo!
Milo Alistair or Milo Poseidon - Milo is one of those names I'm just not sure about my opinion on. As much as I love Greek mythology, I just can't see Poseidon working, even as a middle. Maybe it's because of the super godly background, I don't know. But Milo Alistair is really nice! I'd kind of like to see Alistair as a first though... Julian and Alistair would make a handsome sibset
Elias Gabriel - I really like Elias, but the -s ending makes it kind of offbeat and hard to pair. Gabriel is alright, not exactly my style but definitely not bad. The flow is okay but could probably be a tad better (maybe another vowel-starting name as a middle would flow better?).
Derek Apollo - Derek is just one of those names I've never been crazy about, sorry. And it's funny, I mentioned Apollo above before seeing it was on your list. I do think it's a bit more usable than Poseidon, and I'll admit that twins/siblings with names of the twin gods would be really cool. Overall, I think the flow is a bit awkward with this combo too.
Ace Logan - I really like Ace, although I prefer it as a nickname. Logan is nice too, but I'm not sure it fits as well in the middle spot (I could see Derek and Logan as brothers). I think that with a short name like Ace, it might flow better with a longer middle -- something about the flow is just a bit off here.
August Adam - I absolutely adore August on boys. Adam is handsome too, but I'm not crazy about the alliteration here, it kind of throws off the flow (but August is also a bit offbeat on its own, so maybe that's it). I think August could make a handsome middle too - no matter where you put it, it's a great name. As much as I like Julian Anchor, I think Julian August would be handsome (but possible a little too Roman? Idk).
Boston Leo - I'm iffy on Boston. I could definitely see it as a middle, but I'm not sure about it in the first spot. Leo is definitely one of those names that always feels like a first, so it's a little awkward as a middle. I think Leo Boston would be really great though.
Jonas Maverick or Jonas Aries - I'm not that big on Jonas, because I like Jonah a bit more and my brain always wants to say Jonah instead. I think Jonas might make a good middle, though. Maverick is nice as a middle, but it feels like a bit of a mouthful when paired with Jonas. As for Aries, I'm not a fan in general, but I would prefer the spelling Ares, which is the spelling that alludes to the god of war and to me looks much more masculine than Aries. Overall, I'm not really liking either combo here very much, sorry.
Ren Alexander - I really like Ren, but it feels very nickname-y, like it needs a longer full name. That said, I really like it with Alexander here. Alexander is one of those handsome classics that makes a perfect middle.
Anakin Skylar - Sorry, I just can't get on board with Anakin. Also, I'm not a fan of Skylar on either gender. Sorry.
Talon Evander - Not a big fan of Talon, because the association with claws is not one that I enjoy. Evander is really handsome though.
Tate Aries or Tate Jupiter - I like Tate, and could definitely see it working well on a little boy (and any age). I think the combo feels a little too short when combined with Aries, and the flow is better with Jupiter, but I think the association with the planet is a little too strong for my liking. Tate Evander would be handsome.
Caspian Remus - I love Cas names for boys, and Caspian is no exception! I like it with Remus here, and I sort of like Remus in general, but the story behind the name isn't that great, since his brother killed him out of greed and all. Still not a bad name, though.