Okay. I know this has been done before but I just felt like telling people a bit about what I thought it could be. It obviously won't be the exact truth but a girl can hope. And, in this case, spread her guesses around fanpop despite the lack of time to do so.

Well, here goes nothing.

Bobby
"Bright fame"
Well, I think he can be a son of Athena or Apollo, since the bright above can mean intelligence or luminous. I don't know why but Apollo fits better in my mind.

Reyna
"Queen", "Pure", "Summit"
Out of all of them, this character is certainly the most discussed of all. Who is Reyna, after all? Who is this girl that seems to signify the end of the Jason/Piper relationship?
Well, of couse I won't be the one to answer this questions, but I'd like to give it a shot as well.
Reyna has different meaning in different places around the world. Summit and reyna both point to a madami royal position, while Pure simply throws me off - I don't have that big a knowledge of the gods and godesses.
Still, I don't think of Hera or even one of the big three when I think of her.
In the roman imperium, Mars was also considered of great importance. segundo only to Jupiter. This leads me to believe her royal name to be a reference to her father's place in the roman mithology.

Gwendolyn
"Fair bow; blessed ring"
Okay, this was one of the hardest ever to find a relation. I thought of Apollo and Artemis (as a hunter) but it just didn't fit in my mental image of them. So, I went a little deeper - and, possibly, a little crazy. Wendy is short for Gwendolyn. And I hope everyone remembers who Wendy is. Yes, I'm talking about Peter Pan's Wendy. The Wendy from the tale where kids go to a place where they can be forever young. And, so, I came up with the idea of her as the daughter of Hebe (Juventas).
BUT, as you might have noticed, I don't accept easy explanations. So, I started to think what was really Wendy's importance in Peter Pan. She was the one that made the choices. Which reminded me of that two headed freak, Janus. I know it's a bit crazy but the whole daughter of Janus thing just clicked when I was molding my Son of Neptune story.
Just recently, though, I found out another possibility. Daughter of Hecate (Trivia). It came to me when I was pagbaba about the name and discovered it was the name of Merlin's (the great sorcerer) wife. Still, I'm not getting into details with that one.

Dakota
"Friend", "Ally"
Well, there's always Philotes, a minor greek god, representing affection and friendship, whom I'm not sure to have a roman counterpart. The problem is that it just doesn't make me satisfied.
The name can also mean "forever smiling", though I'm not sure what that can represent. We can also think about Aphrodite or Felicitas (romans do like their names easy and latin, hun?).
Strangely, after pagbaba about the name, I just can't help but to think of Juventas and how youth is always a time of joy and kindness (at least in theory).

Hazel
"Hazel tree"
The obvious choice for this one is Ceres, Baco or Faunus since the name Hazel makes a direct reference to nature. And that, of course, doesn't satisfy me.
I think the real reason behind my constant insatisfaction is that there are already too many children of normal gods. We are in need of minor gods presence as main characters.
Anyway...
Hazel puno made me think of wand and wand made me think of magic, which made me come back to Trivia (Hecate). Yeah, I know I'm tripping, but it just clicks for me to have Hazel as this magical, very nature related being.

That was it, guys.
I hope you enjoyed pagbaba this as much as I enjoyed Pagsulat it. Please, pardon my abnormal informality and my idiotic rants. madala with me, okay?
Reply telling me your opinions and if you agree with my crazy guesses.
No flames, I beg.