I'm afraid I don't have a specific answer for you, but it seems possible that your Adam is descended from, or at least related to, the Jacob STRAUB/STROUP who appeared in NC by 1771:http://dgmweb.net/genealogy/Straub/FGS/JacobStroup-MariaCath...
As for the name, the original surname is German STRAUB. Most STRAUBs had the spelling of their surname Anglicized to STROUP, some went as far as STROPE or STROPES. STRAUP and STROUB are less common variations. The main STRAUB branch that became STROPE/STROPES was the earliest (as far as I know) STRAUB immigrant to America, specifically, Johannes STRAUB, to New York in 1710. One branch of his descendants, surnamed STROPE, then settled in Bradford Co., PA, and another in Greene Co., PA. I do not know if any of these STROPEs went south to NC, but it seems unlikely, so your Adam probably has different roots (as above).
Sorry I couldn't be more help. I have a web site dedicated to STRAUB/STROUP (and variations), but I have concentrated on those with "Pennsylvania Deutsch" origins. I have rather neglected southern STRAUB/STROUP. The home page, with index and search engine, is at:http://dgmweb.net/genealogy/Straub/StraubHome.htm