How to manage all these identities though? How to make sure they don't leak into each other?
This is not always possible if one means not just daily use name but also legal name.
There is at least one state where the name change law allows residents to only change name once (except for marriage related last name changes).
It's a lot easier if you share an IP with a hundred other people, such as with a VPN or CGNAT or many schools/businesses. Then you can just reset the cookies you want without it being able to fall back to another unique identifier.
This isn't even considering device fingerprints such as created using html5 canvas or audio APIs.
I don't do this myself, I'm just saying there's a lot more to it than picking a new HN name.