You can only close an account on HER from inside the app. You can do so by going to:
iOS - My Profile > Settings in the top, left hand corner > Scroll down to Support > Select Close Account.
Android - Go to "..." in the top, right hand corner > Support > Close Account
When you close your account it will delete all your profile data. Your account will no longer be visible anywhere inside of the app.
If you choose to join HER again you will need to create a new account, as once accounts are closed they cannot be reopened.