Changing Azure User Access Administrator?

There are several terms:

  • Azure AD tenant (something.onmicrosoft.com) that is directory of all users. In properties you can set that all users with "Global Admin" role have access to all Azure subscriptions.
  • Azure subscription, has owner of user, this can be changed using portal.azure.com or via support ticket. It is typically user from organization (Azure AD tenant) in charge of the project / payments.

You can add additional users (free) in Azure AD tenant and provide access permissions to Azure subscription or resource groups (using IAM)