It's most of his name. Long before his full name became common knowledge, you could already Google "Scott Alexander psychiatrist" and find him almost instantly.
There are ~50k psychiatrists in the US. Roughly, 1 in 10k people in the US is named Scott. Mathematically, that means knowing "Scott is a psychiatrist" brings you down to ~5 people. Even if we assume there's some outlier clustering of people named Scott who are psychiatrists, we're still talking about some small number.
Surely adding in the middle name essentially makes him uniquely identifiable without an other corroborating information.
Seems to be more like one in 425 per SSA.
The magnitude is so small that anonymity is essential broken.