It can be done easily (I'm not sure that Geni loves it but it works...)
add the first profile as your son and the disconnect him from you - this way you have a "stand alone" profile.
make sure you intend to maintain the other tree and not just "add and forget"
this is much better than faking a new user
Private User - bookmarking is a feature in the browser you are using, and the suggestion is just a reminder for your self where that tree is because there is no option in Geni to bookmark profiles anymore or display unconnected managed profiles.
If you have added the profile yourself you are by default following it, unless you have removed following, but to avoid the extra step to enter the name to search for it a bookmark in your browser is probably best.