How do you discard empty prescription bottles with privacy in mind?

Someone brought this question up to me recently and it was something I never thought about before:

If you don’t want anyone to know you’re taking a particular prescription medicine, but your name is printed on the bottle, how do you discard it so that your privacy is protected?

And while we’re at it, how do you hide your bottles/pills so that no one finds out what you’re taking?

Looking forward to hearing some creative answers!