The full names of the two cousins are very close:
Caroline of Parma: Carolina Maria Teresa Giuseppa
Maria Theresa of Naples & Sicily: Maria Teresa Carolina Giuseppina
Caroline of Parma was named after Charles III, Empress Maria Theresa and (perhaps) Joseph II. I presume Maria Theresa of Naples was also named after Empress Maria Theresa, Charles III (or maybe Maria Carolina herself?), and Joseph II. If Maria Amalia had her way, Caroline's names would've been Maria Teresa Carolina Giuseppa. It would've been more confusing! And both girls took after the Bourbons in looks (although they never looked exactly alike, except maybe for the Bourbon nose)!