Caius Martius earns himself the nickname "Coriolanus" after wasting an enemy city called Corioles. Pretty impressive, if you're into wasting entire cities, that is. This nickname tells us that Coriolanus is a big, bad warrior who should always be associated with his military skills. In fact, his successful military career defines him as a character.
Some characters in this play don't even get a proper individual name. The Roman plebeians are just "Citizens," not even important enough to have individual identities. We get the sense that they're just one, big, rowdy mob ready to get its riot on at a moment's notice. That's also why they're so often referred to as simply "the rabble."
One last thing. You probably noticed that all three women characters in the play have similar names--"Volumnia," "Virgilia," and "Valeria." Literary critics like Marjorie Garber like to call these ladies the "three V's." You know what else starts with the letter "V"? The word "Vagina," that's what.
What's up with that? Well, these V names further align each of the characters with the female body--especially the maternal body. With, Volumnia this association reinforces the idea that her role as Coriolanus' mother is the most important one in the play. (Like how she's always running around reminding everyone that Coriolanus is "the only son of [her] womb".) After all, Volumnia plays a huge role in shaping her son's character and has a lot to do with his tragic fate. See "Themes: Family" for more on this.
One more thing: in Latin, the word vagina translates to "sheath." Hm. A bunch of men running around waving swords, and a bunch of women sitting at home being sheaths. What do you make of that?
There are two major social classes in this play: patricians (the powerful aristocrats who run the government) and the plebeians (the lower class "Citizens" who have little to no power). The plebs are always portrayed as fickle, unruly, and cowardly. The patrician warriors, on the other hand, fight bravely and earn a lot of honor on the battlefield.
But then, the patricians who run the Senate are pretty manipulative and don't necessarily have the peoples' best interests in mind. So, it's hard to tell if Shakespeare's play ever really takes sides on the whole Occupy Rome thing.
Coriolanus is a grown man with a wife and kid but he's still submissive to his mom, which suggests that he's emotionally immature. When he gets booted out of Rome, he swears off his family entirely and tries to pretend that he's alone in the world … until his mom, wife, and kid show up and beg him for mercy. Turns out Coriolanus is kind of a softy when it comes to his family because he changes his mind about demolishing Rome and arranges a peace treaty.
Volumnia manipulates her son and bosses around her daughter-in-law, which shows us that she's domineering and likes power. She also brags about raising her kid to be a killing machine and gets off on seeing his battle wounds. In other words, this is one mom who's leaning in … or at least leaning on her son.
Virgilia, on the other hand, is a loving wife and doting mother. She hates to see her husband go off to war but keeps her lips zipped in front of him. Basically, she's what Shakespeare's 17th century audience would have considered a traditional good wife: silent, obedient, and chaste. Check out "Themes: Family" or "Themes: Gender" if you want to think about this some more.