I get some emails from Stack Overflow that are about specific non-Stack Overflow sites, such as one. This was all checked on the email talked about here: the email address is
email@example.com, the name that shows in Gmail is "Stack Overflow", and the icon is the Stack Overflow logo.
This is kind of weird. It should probably be changed some time either so that emails about non-Stack Overflow sites on the Stack Exchange Network are from either specific emails for the individual sites with their logos and names or they come from a general email for Stack Exchange with the Stack Exchange logo.
This could be good to avoid confusing new users; if someone never used Stack Overflow and only used other Stack Exchange sites they could likely be quite confused due maybe not having any idea what Stack Overflow is and/or not knowing that it is part of the same company.
If they came from different emails for each Stack Exchange site, then it might make it easier to keep track of them, such as marking some sites' emails as important and others as not important.