In my experience, "considering firing" somebody is usually bogus. So what did the boss do, call the person in and say, "I'm CONSIDERING firing you, Poophandle. I don't like your new name." While that would be really really dumb of them to do, there would be very little you could do about it. What, does he(the boss) expect you to "unchange" your name to avoid being fired? That's not reasonable.
It's possible that this person has heard the boss say, "I oughta fire her!" and someone has shared this with her, and your friend has taken it far too seriously. I don't think there's much to worry about.
If she is fired for this reason, the first thing she would need to do is file for unemployment benefits. While they may fire you for any reason, if they cannot show that they had a valid work related reason to terminate you, they cannot stop you from receiving unemployment benefits if otherwise eligible. Then you take it up with EEOC. But something has to have already happened, you can't file a grievance just because your boss has threatened to fire you.