The Sea of Atlas was named first, in The Histories of Herodotus.Austin wrote:A good thing for anyone to research if one has the time is whether the Atlantic was called the Atlantic at the time, and how far back before Plato wrote about it was it first used or named. Point being; i doubt the Atlantic Ocean was named after, in honor of a "mythical" island from a "fairy-tale" story.
The man who named Island of Atlas wasn't born for another 25 years, probably (there's a little ambiguity, just to make our lives interesting).
The first part of its name refers to the Atlas of Greek mythology, making the Atlantic the "Sea of Atlas". The oldest known mention of this name is contained in The Histories of Herodotus around 450 BC.
Before Europeans discovered other oceans, the term "ocean" was synonymous with the waters beyond Western Europe that we now know as the Atlantic, and which the Greeks had believed to be the gigantic river, Oceanus, encircling the world.
Atlantis (Greek: Ἀτλαντὶς νῆσος, "Island of Atlas") is the name of a legendary island first mentioned in Plato's dialogues Timaeus and Critias.
In Plato's account, Atlantis, lying "beyond the pillars of Heracles", was a naval power that conquered many parts of Western Europe and Africa, over 9,000 years before Plato's own time — approximately 9400 BC. After a failed attempt to invade Athens, Atlantis sank into the ocean "in a single day and night of misfortune".
Some scholars argue Plato drew upon memories of past events such as the Thera eruption or the Trojan War, while others insist that he took inspiration of contemporary events like the destruction of Helike in 373 BC or the failed Athenian invasion of Sicily in 415–413 BC.
That was all courtesy of Wiki.
So, the first reference to the Sea of Atlas was in 450BC, and the reference of Island of Atlas would have been 373 BC, 415-413 BC, or 9,400 BC. I hope that has cleared things up for you!