I would much rather fill the Internet with my own content about myself, than leave it empty for someone else to impersonate or disparage me. Additionally, I am proud of what I post publicly — otherwise I wouldn’t post it.
Public personas are a professional necessity, especially in our industry. For example, what if you want to show your contributions to open source? Or your stackoverflow answers?
If you do everything online under a separate identity, then all your positive contributions are unlinkable to yourself. Yes, you can hide any “bad things” you may post from your employers. But are you really posting anything bad? Is it worth sacrificing credit for your positive contributions?
Granted there is always the “nothing to hide” counterargument. That is, it’s not up for me to decide what’s “bad.” A potential employer could misinterpret my words, or otherwise negatively judge me based on my online profiles. But in that case it’s probably better to avoid the relationship anyway.