Username (that's publicly facing) should always be user customisable. That's self evident in the fact that it's called the "USERname".
So whilst it's perfectly ok to use an email address as the login name, the publicly facing username must be entirely and absolutely editable at signup, and the user must be clearly informed as to what will be shown as their username (to the general public) long before it is first shown.
This is basic, decent and common sense consideration of users and their right to privacy and control of their public image and identity in any space, place, forum or other online entity/platform.
See the many (very legitimate) concerns and contentions regarding the "real name policy" and online ID issues of Facebook for how badly this can be handled. They can get away with it because we seem to have accepted their right to be totalitarian arbiters of web ID. But that still doesn't make this type of behaviour right.
Apologies for Wikipedia link: https://en.wikipedia.org/wiki/Facebook_real-name_policy_controversy