Private User,
As far as i know that is completely impossible. But for all practical purposes your profile acts in many ways as a Master Profile (i.e. if there's a merge, then the other profile is always merged into yours, and not the other way around).
If you want it to be publicly visible, all you need to do is set the privacy, and i see that you have done that already (i can see your name just fine)
Check your https://www.geni.com/account_settings/profile_privacy page, - by setting most information as public your profile almost acts as a locked Master Profile, except of getting listed as the most popular master profiles if that ever would be an issue.
Since this is a world-tree where people who usually would be listed as Master Profiles because they are "famous" also should be allowed to be Geni users we, to avoid having a duplicate sibling as a MP, ask them to open up for the information that should be public, for example at least showing the About me where you usually link to wikipedia and other public info.
Private User -- the MP designation for living people is for famous people, or people whose profiles need protecting for some other reason.
Usually the MP designation is used for profiles of deceased persons. It can be use to keep a profile safe, to mark the main profile with the best information, into which other profiles get merged, or for other reasons.
The thread title is confusing, because it says "My" profile. But that doesn't mean "the profile of me." It means "the profile I have been working on."
Nicholas James Vetrovec, all set. Note that I added 1) his display name, 2) his place of birth, and 3) his occupation. If we can find his exact birth date, that would be great to add!