In Uncle Vanya, most of the characters are related to each other, but the way they deal with their relationships tells us a lot about them. For example, Serebryakov feels a certain allegiance to Yelena and Sonya, and while he's friendly with Mariya and Vanya, he doesn't seem to feel obligated to them:
SEREBRYAKOV: [...] My life is now over, I'm not thinking of myself, but I have a
young wife and an unmarried daughter. [...]
VOYNITSKY: Exactly. You'll sell the estate, excellent, a splendid idea… And where would you like me and my old mother and Sonya here to go? (3.332-56)
In the end, Serebryakov only feels that he owes his care to his blood relative, Sonya, and his wife, Yelena. The others, who were actually his first wife's relatives, are pretty low priorities for him. It's another way in which all these weird relationships are kind of unstable. You never really know where you stand, but you can bet you're going to be unhappy about it, however it goes.
Even though the whole play takes place at the country estate, there's a big difference between the characters who live there year-round and the city folk who are just there for fun. Serebryakov puts it bluntly:
SEREBRYAKOV. [...] I cannot go on living in the country. We are not made for the country. (3.335-36)
What he means is, of course, that he and Yelena weren't made for hard work. Everyone else busts their bums making sure the estate produces enough to line their pockets enough to stay afloat. Serebryakov and his wife, used to the city, just watch the profits roll in.
A woman so beautiful that she causes a war? Well, maybe not a war, but at least a brawl between Ivan and Serebryakov, with a little bit of roughness from Astrov thrown in… We're talking about Yelena, of course, and her namesake, Helen of Troy. Just like the face that launched a thousand ships, Yelena is just too good-looking for her own good. She drives everybody wild.
And if Yelena is special, Vanya is the exact opposite. Short for the name Ivan, which is basically a Russian equivalent for John, Vanya is a very common name. It's actually the most common name for a Russian man to have. It's so common it's almost like being called John Doe, if you get right down to it. So Vanya's utter ordinariness, complete lack of specialness, is emphasized by his ordinary name. And yeah, if you've got the idea that "Uncle Vanya" pretty much translates as "Uncle Johnny," you're right on track.
Uncle Johnny. Ouch.