The operative word here is should.
This naming convention is by no means mandatory. And it also has nothing to do with being able to see who created the library.
The point is that there is a single flat namespace for packages, and that thus every package ever written, including old packages that are no longer maintained, packages that are currently being written, packages that haven't been written yet, packages by developers who are already dead and future packages of developers who aren't even born yet, shares the same namespace. So, every developer has to agree with every other developer, including ones that are already dead and ones who haven't been born yet on what the names of packages are going to be.
Obviously, this level of coordination is impossible. So, the next best thing is to have some sort of registry where every package name must be registered and the maintainer of the registry ensures that package names are globally unique.
However, doing that is quite expensive, so instead they instead chose a naming convention which "outsources" the maintenance of this global registry to someone else: by suggesting that the package name should be derived from an Internet Domain Name you own, the work of making sure that no two people own the same package name is outsourced to the Internet Domain Name System which has been reliably, effectively, and efficiently doing exactly that for decades, on a global scale.
Now that you understand what the naming convention is for, you can probably answer your question yourself:
Should I unpublish and republish with a proper package name?
Yes, you should, but not for the reason you are asking about.
In how far will I run into (legal) issues (if any), because I am not the owner of health.com (example).
You won't run into any legal issues, probably. (However, as always, ask a lawyer. This is a programming site. We understand programming issues. We don't understand legal issues. That's what lawyers are for.)
The issue is that you cannot guarantee that your names are going to be unique. The owners of health.com may decide to create an Android app, and they may have the same class names as you, for example. By using a package name that is guaranteed to be unique, e.g. a domain name you own (and even if it is just