I would say it would evolve into soccer (football, for non-Americans).
The reason it is difficult to defend the goal in basketball is "it's way up there". It's impossible to simply plant yourself in front of the goal. Soccer goalies plant themselves in front of the goal, but their difficulty is that the goal is big. In 3d, zero-gravity, a basketball player can easily plant herself in front of the goal, so the game would have to have a larger goal to make it continue to be interesting.
As someone else pointed out, you can't dribble in zero-gravity, and you can't measure steps the same way you can in basketball. The most obvious way to keep the ball in play would be to rule out holding the ball at all. Hence, kicking. Ergo: soccer.
As others pointed out, you'd make the walls of the arena out of transparent aluminum and the audience would watch from all around, outside. You'd need some sort of technology to allow the players to anchor their hands/feet to the walls and probably also to attract them back to walls.
I'd recommend a spherical arena as that would lead to interesting bank shots. Maybe ovoid, to stretch out the play area. Prolate obloid would also lead to better bank shots than a sphere. Maybe even attenuate the ends of the ovoid so the goals are close to the foci of the ovoid.
I think this sounds like it would be an awesome sport to watch. Players doing spinning kicks that send their bodies recoiling back would look awesome.
Assuming they don't kill each other. Keeping track of other people in 3d is a lot harder than in 2d, and if neither player is touching a wall, it would be difficult to avoid a collision once you were both launched. Maybe players would wear belts/suits that would automatically detect/mitigate collisions.
Some sort of flight suit would allow for more interesting play. Having players stranded out in the middle of the arena, trying to swim through the air would be silly, but ultimately boring. You'd want the players to focus on pushing off walls (each other?) to get speed, but some ability to correct path/avoid serious injury would be good.