Since most processing programs clear the screen at the beginning of the draw() loop with a background() call, all you need to do most of the time is just stop drawing the shape. In some cases this may involve removing an object from an arraylist or whatever. You can draw strings to the screen with text(). You can align text with textAlign(). You can find these and many more methods in the reference and you can learn how to use them with the examples that come with Processing. Good luck!

I don't know your background, but you seem to think in objects.
That's great, but Processing itself is mostly procedural, low level.
If you want objects, like rectangle with text in it, you have to code them yourself.
It is a bit annoying, although there are libraries doing this for you, but it is educative, as you learn how such entities must be made.

Side note: if you can show some bits of code illustrating what you try to do, we can understand better your goal.