On September 23rd, 1493, Cristobal Colón, who was on his second trip to the "new world," had made it to what is now the island of Guadalupe. While there, he came upon some Taino natives who had been taken prisoner by the Caribs of the region. These captives managed to convey that they came from a bigger island further up the Antilles archipelago, an island they called Boriquén (roughly: 'the land of the brave lord'). They begged Colón to take them back to their island. Colón had arranged it with the Spanish crown that he would be the de facto governor of all of the territory which he "discovered" in the name of Spain, so it's not surprising that he would grant these native captives their wish. He wanted to return to Quisqueya anyway, which he had first visited in his famous first voyage, so claiming another isle on the way sounded like a good enough idea.
On November 19th, Puerto Rico was sighted. Colón named the island San Juan Bautista and they landed on the west coast, near what is now the town of Mayagüez. But Colón was sufficiently burdened with the tasks of establishing the colony at Española (the name he had given to Quisqueya) to stay long on the island. After a stay of only two days, he hurried on westward, leaving its dumbstruck Taino population to scratch their heads in wonder and awe at this development in their theretofore unchanging existence. (These two days, incidentally, were the only two days that Colón ever spent on territory that would eventually become American —i.e. USA— soil.)
Some fifteen years would pass with the Tainos of Boriquén having no further knowledge of these god-like (or so it seemed) creatures from the sea. Worse, if they had any information coming in about them, they were getting it from their neighbors and kin over in Quisqueya, and the news were not encouraging, I bet. They were undoubtedly stories of enslavement and of occupation and oppression and disease. Despite some efforts led by Catholic priests to protect them, the Tainos suffered greatly under the Spanish conquest.
Finally, in 1508, Juan Ponce De León, who had been a soldier on board one of the seventeen ships that comprised Colón's second voyage, and who had since moved from Spain to Santo Domingo (on Española), was commissioned to return to San Juan Bautista with a crew of fifty men to colonize the island. He arrived on August 12th, landing on the southern coast near Guánica. Making his way through the lush mountainous island, he finally arrived at the northern coast, where he found a magnificent bay. The minute he glimpsed this bay, it is said that he exclaimed, "Ay, que puerto rico!" ('My, what a rich/delicious port!').
. . . . which finally brings me to the riddle . . .
How did the names of this rich port and of the island of San Juan exchange places so quickly? Not long after Ponce De León exclamation, the island was referred to as Puerto Rico and the bay was referred to as San Juan.