I just changed the account from which we send JIRA outgoing mail, if only because I was able to configure incoming mail with the new account,and I would like people to be able to "reply-to" and have comments added to their issue.
Since I made the change, the Display From went from "Davis, Shannon (JIRA)" for example to "Enterprise JIRA", which is the display name of that mailbox. It was nice because I could see who had made the issue change, or added a comment, and then I knew whether I really had to read that or not.
I can't see any way to get it back, nor did I change anything beyond changing the account.
I am on version 6.3.12 if it matters.