NOPE, Rhode Island has nothing to do with the Greek island of Rhodes or with Rhodesia.
Adriaen Block from Amsterdam, nickname Arjen, was the first to see it, from his ship. It was the fall of 1614, the leaves were turning red, and Block was busy mapping the coast of America.
Four times he sailed back and forth across the ocean, long before the Mayflower, between 1611 and 1614, and during the last trip his ship broke in two, just outside Manhattan. The crew, with the help of Indian boys, made a new boat (and, with the help of Indian girls, also made a whole bunch of babies, which is why many Lenape Indians still walk around with surnames like DeGroat, DeFreese and Van Dunk), and Captain Block christened that boat, understandably, The Unrest.
With it, he inspected the coastline north of Lange Eiland, now Long Island, and was awed by the fall foliage that colors America bright red and orange. He discovered a river and named it River of the Red Hills, docked at an islet still called Block Island today, crossed over to the mainland and saw how beautiful the coast looked with all those fall colors. To top it off: the clay was red, too.
Roode Eylant is what he called what he saw. And it’s still named so today. Rhode Island.
* In the center of the map drawn by Arjen Block is Roode Eylant. Bottom right, in the water: Adriaen Blocks Eylant.