What is my username

Edit: Wrong answer earlier.

Maybe the username you are referring is the friend code. Go to friend tab and tap search. You will see your friend code there. Also, you can see it when the FGO title appears, it is written below.

I was also confused about it.
I even wrote to support saying there is no sign in option so what happens if something happens to my phone.
I didn't get an answer.

Later I saw there is a specific number for friends to send friend request.
Since that number is for your account only, I believe this is our specific user name for the account.