I don't know if my Moody family links to yours or not but I sure do have all of those names either in my collateral family lines or in the Other matching surnames from my Dad's DNA reports. Anderson is a name that we have matches to several times, Rankin appears in a branch of my Moody family, White (probably spelled Whyt a long time back), and Henry as well.
My Moody family probably came from the Moodie family of the Orkney's and Caithness, Scotland whose branches trickled down to Aberdeen, Dundee and the Edinburgh areas.
We have the most other Surname matches to families in the Angusshire area of Scotland.
My family appears to have left Scotland and gone to Northern Ireland and then to America sometime between 1718 and c1770. I also have a branch of Moody family in the Annapolis Co., Nova Scotia area as well (from DNA match).
I see that you posted this a long time ago so you may not still be here, but if any of this seems like it might be a fit, let me know.