I’m recently new to Plusnet mobile and I believe you should get an automatic email link to your new account with temp password when you start a mobile contract. No registration is required as such. You need the supplied details for online or via the app.
I didn’t get the email, however, so just went to the sign in page for mobile account, clicked on forgotten password, entered the mobile number in the username/mobile number box, and the email associated with the mobile contract order.
This allowed a reset of the temp password I never got, and thereafter all my details, contract details, etc., were there when I first logged in. I was given the actual Username allocated to me via a phone call to support for an unrelated matter sometime after that - the allocated username is only really needed if the use of the mobile number fails for some reason. As I hadn’t got the original email I had never been given the username before that phone call.