At our university, the SIS_ID displayed in the People list and the Secondary ID displayed in the Gradebook are number-strings that are useful for big databases to match identities. We also have a username that is much more human-friendly and that also forms the first part of our institutional email addresses. That username is not displayed in any list or tool in such a way that an instructor can use it to ensure that the person whose record she is looking at is, indeed, the person she thinks it is.
A solution for us -- and we think others might find it useful -- is to allow the default email address to display in the People list. The address should also show up in Groups tabs and similar locations.
Ideally, which course roles can see the address would be controlled by the institutional admins.