Possible, yes. But not equally easy.
It's not like he was trying to hide from the NSA or anything. The goal was "I don't want my patients to see my blog on the first page of Google results when they search for my real name". The NYT completely obliterated that.
Additionally, the fact that the NYT chose to smear him means that now many potential patients may google his name, see the hit piece and nothing else, and decide "yikes, better not go there".