Knowing the meanings of the names of the people around you can also give you some subtle (or, in some cases, not so subtle) clues to guide you safely through your narrative.
Oddly enough, known figures in mythology tend to ignore these clues, often to their extreme disadvantage. After all, how many people decided to spend the night at the house of a man called Procrustes (the Stretcher) only to find themselves stretched out to fit the bed in his guest room, laying there all in pain and all, 'WAT HOW DID THIS HAPPEN?'
And Priam, King of Troy, when the city was in its final day and being sacked by the Greek troops, somehow thought that Achilles' son, Neoptolemus, would abide by the rules of decent, traditional warfare, when obviously the kid was born for a New Sort Of War.
Now, Heracles, to be fair, might have an excuse for being skeptical about this whole nomenclature thing. He was born the Glory of Hera, after all, and Hera has done nothing but plague him with labors and troubles for his entire life, up to and including driving him mad and making him kill his wife, Megara, and their children. But think about it for a second; step back and be circumspect. How much glory would Heracles have had... without Hera? Without Hera, no labors, no trials, nothing but an uneventful (and unremarkable) life. Maybe if he'd thought of his name in that sense, he might have changed his mind and begun to pay attention to the names of those around him. Let's see how this insight might have changed the tragic story of his second marriage to Deianira, daughter of Oeneus. Here's the story as it stands.
Heracles the Blockhead:
Heracles: Woah, who's the hottie?
Oeneus: That's my daughter, Deianira!
Heracles: Awesome! I'll take two!
Achelous: No mine!
Heracles: *murder*
Nessus: No mine!
Heracles: *more murder* Awright, that's done. I've got a couple labors left to wrap up, so, uh, see you in a couple years, babe. Keep a light on for me!
a couple years later
Heracles: I'm home! And look at this hot chick I brought home with me!
Deianira: *murder*
Heracles: FML. *ded*
Now let's see how it runs with a little knowledge of Greek nomenclature.
Heracles the Enlightened
Heracles: Woah, who's the hottie?
Oeneus: That's my daughter, Deianira!
Heracles: 'Man-Destroyer,' huh?
Achelous: No mine!
Heracles: All yours, dude.
And let's just imagine how much trouble Thebes could have been spared with a little conversation along these lines:
Jocasta: Oedipus? That's an interesting name. Why do they call you 'swollen foot'?
Oedipus: Oh, evidently when I was a baby I got stabbed through the ankles with a spike, somehow. I spent most of my early childhood getting over the injury.
Jocasta: That's a weird coincidence, I once had a baby that I tried to get rid of by stabbing a spike through its ankles and throwing it away in the woods.
Oedipus: Huh. Y'know, I never really //was// sure I wasn't adopted...