Themistocles means "Glory of the Law." It's a fantastic name! It's also a rare one, and it makes me wonder why his father gave it to him. The answer may lie with Neocles himself.*
Neocles means "New Man." New to what? We can only speculate, but perhaps it has something to do with the period in which he was born.
If Themistocles was born around 525 BCE, then his father (assuming he got married and had children between 20 and 30) was born around 550 BCE. It was at this time that many poor Atticans were forced into a form of indentured servitude. A family struggling on a farm could not mortgatge their property for a loan. Instead, the farmer would have to offer himself and his family as security, providing some form of labor in lieu of repayment. If he failed to meet his obligations, he and his family could be sold into slavery.
This went on for a number of years, until a noble named Solon recognized the injustice of the sytem and wrote a series of reforms known as Seisachtheia that made it illegal for indebted families to be sold into slavery. If Neocles' parents were affected by these reforms, it is possible that they wanted to name their son "New Man" to symbolize a new and better era.
Yet despite his family's high hopes, Neocles would still struggle under the nobility's yoke. The higher classes barred all but the top men of Athens from holding the most prestigious offices, and ignored the lower classes in the Asssembly. Neocles probably chaffed under these invisible shackles, and perhaps named his son Themistocles in the hopes that would one day the child might bring justice to the people.
Themis was the Greek goddess of divine law and justice, representing the natural order of things. She was one of Uranus and Gaia's children and is one of the few Titans venerated by the Greeks. Anyone who had Themis in their name would be expected to fight for what was right. Themstocles would do just that, but his methods for this were more shrewd than just or fair. Perhaps Neocles would have been better off naming his son Metistocles instead.
Metis was the goddess of "magical cunning", and anyone who was of "bold thought and bold action" possessed her attributes. Themistocles was nothing but cunning. He would lie, cheat, steal bribe and bully his way to the top of Athen's fiercely competative political game, using his metis to get ahead. Although this would prove to be a good thing in the long run, the Athenians did not appreciate Themistocles' daring genius and would eventually ostrasize him after he helped them win the Persian Wars.
*Of course this is all highly speculative on my part. There is no way to know the reasons why Neocles and Themistocles had such unusual names.