Okay, so if you have changed the name to something appropriate then I would do a ban appeal but mention in the title mute appeal. I am guessing they will unmuted you and you will be fine. If your name is still inappropriate change it then follow the same steps.
If thats the case, then change your name if you haven't already, and just make a mute appeal in the ban appeals section as there is no ban appeals, or just PM a mod with reasons why you've changed, etc.