The issue here is that he's a psychiatrist. Dealing with random crazies, some of whom might literally try to kill him if they knew where he lived, is his day job.
So the extra danger from that direction associated with the NYT publishing his real name in an article about SSC is that they might read that article, discover that Xxxxx Xxxxx who treats them for paranoid schizophrenia also has this blog that says yyyy yyyyy yyy yyyyyy and that zzzzzz zzz zzzzz, and then go after him (using the real name they already had).
The harm there isn't zero, but I think it's much less than the harm that results from giving his real name to people who already knew about SSC and hated it for some reason.
(Also, at present at least, it's easier to go from Scott's real name to his blogging pseudonym than in the other direction with a couple of minutes and a search engine. Neither direction is terribly difficult, but that's no reason why the NYT should make them both easier.)
The issue here is that he's a psychiatrist. Dealing with random crazies, some of whom might literally try to kill him if they knew where he lived, is his day job.