I'm going to be passive aggressive and refuse to repeat my name to a customer
Is there a reason you are wanting to be so rude to them?
If they don't listen to me, I won't listen to them.
Be more polite to the customer. Maybe they did not hear your name because it was loud. There is no need to be aggressive towards them.
That is not my fault.
It is your job to make sure the customer has a good experience. By doing this, you will get a bad review and you might get fired.