Panama rhymes with:
arkansas, backsaw, baja, bhiksha, bluelaw, brauhau, chihuahua, chippewa, chutzpah, coleslaw, dada, denwa, duchossois, gadbois, gondwana, grandpa, hoopla, kershaw, livernois, mardi-gras, narasimha, omaha, ottawa, philyaw, quebecois, quebecoise, rorschach, yamaha, zsa-zsa, zsazsa
Panama sounds like:
p.m., pabon, paean, pain, paine, paino, pam, pammy, pan, panam, panamanian, pane, panem, panini, pannone, pannu, panny, paone, papania, papin, papineau, papini, papon, pavon, pavone, pawn, pawnee, pay'n, payan, payin', payna, payne, peine, pen, pena, penh, penman, penn, penna, penney, pennie, penniman, pennino, penny, peon, peony, pepin, peppin, peyman, pham, phan, phen, phenom, phenomena, phenomenon, phinney, phippen, phnom, phone, phoneme, phoney, phony, piana, piano, pima, pimm, pin, pina, pine, pineau, pineo, pinho, pini, pinion, pinn, pinneo, pinney, pinnow, pino, piny, pinyan, pion, pippen, pippin, pm, pneumo, pneumonia, poem, pom, poma, pomona, pon, pony, poon, popham, poppen, ppm, puffin, puma, pun, puny, pymm, pyne