Can doctor's office call your home and leave a message mentioning medication that you're taken by name?

Yes, you doctor's office could do this without incurring liability, if you mean could they leave an answering machine message or voice mail; they were leaving the information at your home, at the number you gave them, and it is not their responsibility if someone else accesses it.

They should not have given the message directly to anyone but you, however, unless you are a minor and they gave the information to your parent. However, even if they did this, it is difficult to see what effective action you could take, since it is unclear whether you could actually recover any money unless you could demonstrate some significant economic injury or consequence due to the disclosure.