Rockingham rhymes with:
buckingham, allingham, bellingham, billingham, birmingham, buckingham, burlingham, burningham, cottingham, cunningham, dillingham, everingham, fillingham, framingham, frothingham, gillingham, landingham, laningham, leadingham, newingham, nottingham, vallandingham, vanlandingham, vanlaningham, whittingham, willingham, winningham
Rockingham sounds like:
rasmuson, rasmussen, rasmusson, reaganism, rosenshine