I tried this when Scott first posted about the NYT article, and the cat was not out of the bag then.
So if a patient had googled "Scott Siskind" before the NYTimes contacted him, they may well have found the post linking the name to the blog.
[1]: https://web.archive.org/web/20200701000000*/https://www.over...
[2]: https://web.archive.org/web/20200701000000*/https://www.over...
[3]: https://slatestarcodex.com/2020/06/22/nyt-is-threatening-my-...