It is possible to change your nickname for a private competition in the options tab of the competition concerned (on the website or from the iOS/Android mobile application).
If you see the "Teams" tab in the ranking screen, you are in a competition where you can join a team in order to have two rankings: one individual, and one team. It is possible to join a team by clicking on the "Teams" tab and choosing the team you wish to join.
You can change your avatar by accessing your profile in the top right-hand corner after logging in, either on the website or the Android and iOS mobile applications.
Yes, you need to enter the platform code provided by your company and then you can register within the Scorecast Business app on Android and iOS.