Selected answers from the Dumb SEO Questions Facebook & G+ community.
Alan Bleiweiss: Create a PBN. Don`t use privacy on any of the domains. See what happens. ! 😜 okay don`t do that. I was being a wise guy, because I just finished a "review" audit of a development site where they were supposed to FIX the issues I found in my original audit, yet where they only fixed some, and made many other things much worse! Sorry.
Alan Bleiweiss: To answer your question, if you are not doing anything toxic from a search engine guidelines perspective, there`s no reason to hide domain ownership. Conversely, if you don`t privatize your info, you`ll be spammed until you die. No positive or negative impact from an SEO perspective.
Doc Sheldon: If you`re hiding some behavior, privacy can be handy. Just realize that Google is a registrar, too... so when it comes to them, there IS no registration privacy. You can keep your identity secret from your competitors, though. ;)
But to answer your question, there`s no impact from an SEO standpoint, either way.