I think it depends on personal preference and what kind of user you are.
If you are going to engage in trolling and just being the kind of person someone wouldn’t want to hire its probably best to hide your identify.
Likewise of you just want to keep it a secret.
My identity has been out there on the internet for a long time. Ran a web community, work in IT. I might delve into grayer topics on social media than on LinkedIn, but I try to check myself and ensure I’m considering others and my behavior before allowing myself to just pump raw emotion into comments.
Not going to claim to be 100% successful at either of those but hey I try.
I limit what information is shared about me as much as I can afford to given the nature of the industry I work in.