Jeff Wallenfeldt writes at the Britannica website:
“Europe existed as a conceptual construct long before geographers began arguing whether there are seven continents or six (the latter model considers Europe and Asia to be a single continent). The ancient Greeks divided the world into three major units: Europe, Asia, and Libya, the last of which referred to the known northern portion of Africa. Those were the divisions that Ptolemy used when he laid out his map of the world in the Guide to Geography (Geōgraphikē hyphēgēsis) in the 2nd century CE. So the notion of Europe is very old, but where does the name come from?
There are a number of theories. Taking a linguistic approach, some scholars believe Europe’s name is descriptive in origin. Those who look to the ancient Greek language to parse it roots combine eurys, meaning “wide,” and ops, meaning “face” or “eye,” to arrive at “wide-gazing” as an appropriate description of Europe’s broad shoreline as seen from the shipboard perspective of the maritime Greeks. By extension, they believe this phrase connotes “mainland.” Adventurous travelers who got closer to the northern lands reported the existence of mountain systems and river basins that were much larger than those of the Mediterranean region, along with climates that were very different from those the Greeks experienced, not to mention expansive primeval forests and sweeping steppes.
Other scholars have argued that the origin for the name Europe is to be found in the Semitic Akkadian language that was spoken in ancient Mesopotamia. They point to the Akkadian word erebu, meaning “sunset,” and reason that, from the Mesopotamian perspective, the western-setting sun descended on Europe. As a corollary, they cite the Akkadian word for sunrise, asu, from which they believe the name Asia is derived. From a Mesopotamian ground zero, the eastern-rising sun would have ascended from Asia.
A competing theory locates the eponym for Europe in mythology, specifically in the many versions of stories about the goddess Europa, some of which date back millennia. One of the oldest versions identifies Europa as one of the Oceanides, the 3,000 sea nymphs who occupied a lower tier in the hierarchy of Greek mythology. Europa was one of only 41 of these minor deities who were thought worthy of naming. Other versions link Europa with Demeter, the goddess of earth and agriculture. Although it is not certain which name came first, it has been presumed that Europa was a local pre-Greek name for an earth goddess, whereas Demeter is a Greek or Greekified name for a more regional deity. In the best-known version of the Europa myth, Europa—the daughter either of Phoenix or of Agenor, king of Phoenicia—was abducted by Zeus, who had disguised himself as a white bull. Zeus spirited her away from Phoenicia to Crete, where she bore him three sons: Minos, Rhadamanthys, and Sarpedon.
No one knows for sure the origin of Europe’s name, but it certainly stuck.”