You should assume that large employers are running your name through some software to see what things you’re posting online. You should at the very least think about public posts and comments under your legal name. Not sure what other services are out there, but I’m sure there are some that can dig deeper than that e.g. attempting to find social media not registered under your name but linked to a known email address. This is the consequence of your data being sold by the Fuckerbergs of the world.
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It’s not just the stuff you see in a Google search. You can personally download your data from websites like Facebook, including a database dump of all your interactions (posts you liked or just clicked on)
The fact is that all this data is out there in a database somewhere. If it’s not explicitly prevented by a privacy policy (and/or your privacy settings) it’s almost certainly being sold to companies, including ones that offer screening tools for job recruiters.