I thought the method was to change your name to something extremely common, like "Janet Brown." A variant is to take the name of some celebrity, so that all the search results are for him or her.
This works. I have the same name as a Pulitzer prize winning author, and it's pretty hard to find me by name. And since I've mostly worked at popular user-facing companies, searching for my name + employer just has stuff about him with share links that use my employer's services. Well except for the guy with my name in Florida who got arrested in connection with using my employer's service.
What's not fun is hearing promos about upcoming interviews of your namesake on the radio and stressing out because you were unprepared for a conversation with Terry Gross.
You can also spam the web with profiles, pictures, and posts from fictional people that share your name. LLMs have made that much easier. It's a pretty common tactic for reputation management companies.
I'm AFAIK ungoogleable, in part because there is a C or D list actor who shares my name, as well as a successful business owner, and apparently a couple football prospects.
On the other hand, the business owner is in the tech space and apparently an early adopter, as he always seems to take the lastname and/or firstlast name, so it's not all roses.
This only helps until someone has an email address or some other detail like where you work. Then you have to use something like Optery which costs about as much as a premium netflix sub