The play could have been called Ivan Petrovich Voynitsky, or Jean, or even just Vanya. But Chekhov decided to call it Uncle Vanya and we doubt that it's just a coincidence. Vanya, the nickname, takes away a lot of Ivan's formality, and even makes the character seem a little childish.
And calling him Uncle means that that's his most important role in life. He's no one's husband or father, even though he'd like to marry Yelena. The title pretty much just magnifies his failure. It also shows that in this play, relationships and how everyone's related to each other are going to play a big part.