The two words are not  related.  Key Largo is a coral cay or reef /low
island from the Spanish "cayo" as native Floridians of a certain age can
tell you.  The island was named by Spanish explorers in the early 1500s
"Cay Largo" literally "large coral island" because it is the largest
island in the Florida keys and in Spanish, the modifier comes after the
noun.  The English pronounciation corrupted the name to Key Largo.  The
English Quay--pronounced Key--is Celtic "cai" and means an enclosure.