It's not a bad way, but you can improve it. Instead of adding an entityName, when you check collision you can verify the type of the obstacle instance:
//If there is an obstacle
if(obstacle != null) {
if(obstacle instanceof Paddle) {
this.invGoingLeft();
}
if(obstacle instanceof Wall) {
this.invGoingDown();
}
}
Also in the second snippet of code your posted you have two if
if(obstacle.entityName == "Wall")
and
if(obstacle.entityName != "Wall")
Consider using "else" instead of the second condition.
Also if you don't want to get lost in your code and follow standards go read about Indentation at http://en.wikipedia.org/wiki/Indent_style .
Is this a good way or would this be considered a bad way to check what it collides with?
I get that in more advanced games where there are more objects and factors etc this would probably be a bad way.
It is a simple game, I think this collision detection is good for a pong game, though if you start making bigger projects, you might consider more advanced techniques which will fits your needs. As for now it's very good to start somewhere less complicated to get more experience.