Buckingham rhymes with:
rockingham, allingham, bellingham, billingham, birmingham, burlingham, burningham, cottingham, cunningham, dillingham, everingham, fillingham, framingham, frothingham, gillingham, landingham, laningham, leadingham, newingham, nottingham, rockingham, vallandingham, vanlandingham, vanlaningham, whittingham, willingham, winningham
Buckingham sounds like:
besancon, bezanson, buchananism, businessman, businessmen, businesswoman, businesswomen