Thinking about Apollo and Athena's names
Athena Cykes. She is named after Athena, the Greek Goddess of wisdom, battle strategy, knowledge, crafts, and much more. Dr. Cykes also shares the name of her mythological counterpart (Athena's mother): Metis.
Apollo Justice. He's obviously also named after a Greek God, Apollo(n). The God of the sun, prophecy, medicine, poetry, music- but most notably: truth and justice.
But: plot twist! Apollo Justice is not named after the Greek God Apollo. He's named after the Roman God Apollo. I know this, because Apollo Justice's father's name is Jove, the Roman name for Zeus.
(If you didn't know, the Romans had a habit of taking gods from other pantheons and incorporating them into their own mythology, adding their own connotations and interpretations. They did so with the Greek Gods, and changed their names. Hera became Juno, Hermes became Mercury, Aphrodite became Venus, ect.)
So, Cykes is Greek and Justice is Roman. Cool, but so what?
Well, the Greeks and the Romans had very different ideas about gods, and many cultural differences.
The Greeks are remembered as philosophers, figuring out the human mind and charting the stars. They were all about math and science. Just like Athena Cykes. Who, guess what, loves the stars and uses her knowledge of people's minds in order to figure out cases.
The Romans, meanwhile, are more often remembered for their conquests. They fought battles through smarts and adapting to their situations, which is something Apollo is great at. The god Apollo, amongst many other things, was the god of knowledge. And invented law. Apollo Justice uses clever battle tactics (perceive) to fight for the truth more effectively.
Essentially, Athena Cykes is Greek and represents Greek ideals, while Apollo Justice is Roman and represents Roman ideals.
(Also: the Romans had quite a few civil wars, which certainly applies to Kurain. Most emperors were extremely corrupt, and Emperor Nero reportedly "fiddled' while Rome burned.' There was a fire that ravaged a good portion of the city, and Nero did little to help. Fires and corrupt monarchies, huh...?)