Nagin rhymes with:
fagin, kagin, beghin, burgin, coggin, duggin, fagin, feigin, flanagin, goggin, googin, hangin', holguin, jungin, kagin, koryagin, kosygin, mangin, melugin, mungin, muskegon, olguin, riggin, rogin, scoggin, scogin, scroggin, singin', wergin, wiggin, zalygin
Nagin sounds like:
nachman, nachmany, nagano, nakajima, nakama, nakano, nakashima, nakasone, nakayama, naquin, nashnamie, nason, nauseam, nazism, neeson, neisen, nesheim, nessen, neukam, neukom, new-mexican, newcom, newcome, newingham, newsham, newsman, newsmen, newsom, newsome, newson, newsum, newswoman, newswomen, nexgen, ngema, nguyen, niacin, niccum, nicen, nickeson, nickname, nickson, nickum, nicoson, niesen, nikon, nishimo, nishiyama, niskanen, nissan, nissen, nisshin, nissim, nissin, nixon, nizhny, noxema, noxon, nugan, nujoma, nukem, nusen, nuzum, nycum