When buying something in an e-shop and verifying myself through Banking IDentity, the George login screen displayed the logo of this e-shop. Is that OK?

Yes, it’s alright. When an e-shop logo appears on the login screen it means that everything runs as it should, i.e. that you are logging into the e-shop service with your Banking IDentity.

Use of the Banking IDentity means the so-called “Ten Security Commandments” must be observed.