The question "naive de Rham cohomology fails for singular varieties" (naive de Rham cohomology fails for singular varieties) recently received an apparently useful answer from a user with the name "Donald Trump." This prompts me to ask what Mathoverflow's position is on fake/celebrity usernames. Certain usernames, such as the one in this example, seem almost designed to spark political controversy, unrelated to math research.
This answer approaches the subject from more of a network level than a MathOverflow-specific stance.
The Stack Exchange Terms of Service deal with this issue as follows:
Under no circumstances will Subscriber use the Network or the Service to ... (c) create a false identity or to impersonate another person....
Subscriber may not (a) select or use as a profile name a name of another person with the intent to impersonate that person.... Stack Exchange reserves the right to refuse registration of, or cancel a profile name in its discretion.
The first statement is quite absolute, whereas the second includes the notion of "intent", which is something hard to judge.
As a moderator on math.se, I would generally only intervene (meaning revert the profile to its neutral
user##### state and clear other fields, and possibly officially contact the user) based on (1) how complete the impersonation is, and (2) how likely is there of confusion. In the case of the aforementioned Donald Trump I find the "impersonation attempt" (if that's what it is) to be rather incomplete (age isn't set to 70, location isn't set to 40°45′45″N 73°58′27″W, and "Sad" isn't used even once in their post). I think it's extremely unlikely that anyone would confuse that profile with the @realDonaldTrump.
While I don't think there is any cause for intervention in the profile in this case, I probably would inspect the user a bit more, and perhaps keep an eye out. I find the profile name and avatar choice to be slightly troll-ish, and would not be surprised if more problematic behaviours are noticed.
I brought this up with the moderation team in email; I haven't heard back explicitly from everyone, but have an idea where most of us stand.
For now no official action will be taken. Putting aside the choice of name and avatar, there has been no detectable untoward behavior coming from this user, and the one post coming from that account so far has reasonable content.
I agree however with the judgment of arjafi that the choice of name and avatar looks trollish, i.e., was likely chosen in order to provoke or annoy some users, and what this means officially for moderators is that the account will in future be watched more closely than it would be ordinarily. Really my advice to the user would just be "knock it off" or "cut the crap" -- this is a community of professional or professionally-minded mathematicians, and as such we have little tolerance for nonsense or games. To the rest of the community, I would counsel not to feed any flames: if it annoys, confine yourself to rolling your eyes, but nevertheless scan for usefulness of content and of course flag any problematic behavior (besides the name and photo).
(By the way, I would feel just the same if the username were "IHateDonaldTrump" with horns coming out of the head: it's exhibiting poor judgment, and is puerile.)
At issue is a sometimes fine line between anonymity (no name) vs. pseudonymity (fake name). In general we prefer, as befitting professionals, that people use their real names and photos, although we respect that there can be compelling need in some cases for anonymity. Pseudonyms are trickier and must be dealt with case-by-case. We have for instance the celebrity name Bugs Bunny, which I consider harmless (and who has demonstrated good mathematical taste and insight). On occasion we see names or avatars of dead mathematicians (Banach, Skolem, etc.), which I find unproblematic, for the most part. Impersonating a living person is much trickier, but in the present case I agree with arjafi's analysis regarding "legality" or official SE matters, and I commend him for citing the official policy. Generally, provided that certain lines are not crossed, I don't think we want to get into the business of being name-police.