How do I have a bank account garnishment stopped, when the person on my account is only there in case of an emergency?

First its not a good idea to piggyback your question on someone else's. This can lead to confusion. You should start a new thread. So I've moved your question to its own thread.

You have to file a motion with the court that issued the garnishment yo quash it. You will have to prove that all the funds in the account came from you and nothing from the other person.