Well lets see...
Admiral Abraxis: Originally, he was Former President Abraxis. But that was too long, and "President Abraxis" was too confusing. Plus, making him an Admiral gave him an extra 'edge'. It was important that he not be a military dictator, though. I didn't want a future society to be oppressive... even in the face of incredible hardship. That's why there is also a civilian government. As for the name "Abraxis", it's a combination of "Abraham" and "Axis". Abraham being a reference to Abraham Lincoln (a leader in very troubled times) and "Axis" being the axis that events revolve around.
Aliana Abraxis: Daughter of the good Admiral, hence her last name. Her first name is inspired by "Aliena" from "The Pillars of the Earth". I didn't want "alien" in her name, though... so I changed the spelling. Also, I pronounce it as if I were saying "Ali" and "Anna".
Dax Joven: Joven means "young" in spanish. So this name is literally "Young Dax". I know a young man named Dax and wanted to put in a little something for him to look at many years from now. That, and I thought the name was cool.
Varro Hale: Varro was a friend and ally of Spartacus in the first season of the Stars series. That's where 'Varro' comes from. It's a good, old, roman name and also used here and there in science fiction. 'Hale' means 'healthy'.
Styglek: This is another combination word. "Styg" is the first part of 'stygian' (as in pertaining to the river styx). "Lek" is an homage to the whovians in the audience.
Thrade: This is inspired by "Thade" in the 2001 production of Planet of the Apes. Our Thrade has nothing at all to do with the character in pota-2001, though. I added the "r" to put a little more edge in the name. But overall the name is ambiguous as to its intent (it could be good or bad)... and this matches the character.
So, sometimes names are about how they sound. Sometimes they are about what they mean, and sometimes they are just completely made up