Making sure your UN and your real name aren’t the same is for your confidentiality. If you have any concerns, I would suggest you flag your own post and discuss it with the admins/mods. They are great at getting back to you.
I am so glad you are talking to your parents. Take the suggestions here to help you in speaking to them. They are very likely your greatest supporters, and it really helps to talk to them. Don’t hold back a thing, and see what they say.
You can always come back here if you need more thoughts.
Given that your teacher knows that there was cheating, the best next step is to come clean. But again, talk with your folks.
It’s hard, we know, but you will get through it. Learn from this!
Best of luck to you!