I think I'm going to get a BlueSky account but I can never decide if I should use my real name or not. So many weirdos out there that I often want to avoid it, but it's also kind of foolish to hide. So, I'm still torn.
I don't see any reason to unless your name is a brand that you're working on in that space.
When I joined twitter years ago, 2009, I used something that was basically my name because that's just how you did social media back then. After a while, I realized that there was no reason at all to have that account associated with me personally. I changed it to a more generic name and profile that reflected my personality sort of, but wasn't me and couldn't be identified as me without some real forensics. Not because I was talking sheet or being bad, but because there was no reason or upside to it and potential risk.
I think it depends on what the platform is and how it's used. Facebook is friends, family, and interest groups - it makes sense to be you. Something like LinkedIn obviously needs to be you (though I wouldn't know I"m not on it). But the twitter style of communicating and interacting with the broader world about ideas, sports, jokes, etc. has no reason to be you - unless you need to be identified with it as a brand for whatever you're using it for.