Isn't it named Europe after Europa in greek mythology.

Also Europe isn't a continent..its a portion of the Eurasian Continent.

Quite so. Zeus went to Phoenicia, transformed himself into a white bull, abducted Princess Europe and took her to Crete on his back. There he changed back to human form and they mated at the beach of Gortyne. She bore three sons: Minos, Sarpedon and Rhadamantos and was given a robot Talos to protect her and the island as present from Zeus. Then she married Asterius, king of Crete who adopted her children.

You can also see another picture of Zeus and Europe on the Greek 2Euro coin.

The story supposivelly symbolizes the transfer of civilization from the fertile plateu in Asia to the new continent, Europe.

The name Europi (Europe) was originally given to central Greece, then it came to reffer to all mainland Greece and then it was extended to all lands of the North and passed to other languages as well.

Yes, that story is quite well known and of course much more beautiful than the more prosaic explanation that it is derived from the word ereb from a Semitic language, meaning "sunset"  as Cywr suggests.

From the point of view from the Middle East, the sun would appear to set beyond the lands to the west. In this regard it may be significant that Eurus is also a Latin term for the East Wind.

Not sure on the "Babylonian" part, but the word is Semitic alright.

The Greek myth names Europe to be from the coast of Phoenicia (Modern day Lebanon).

I agree with Cywr. There was never any definite name until later in Human history for any of the continents. Africa wasn't called Africa, it was part of the Caliphate at one part, so it had it's own name then. And it's own name when ruled by the individual tribes. And it's own name for damn near most of it's history. A movie, though I can't be sure how accurate it was, depicted African Slaves on a boat... the name escapes me at this time, but they didn't even have a name for the area in which they lived. They could find it, but they didn't know what to call it.

Much could be said the same to Europeans. Although, I would just assume it was the "Christian Empire" in its simplest forms.

"Europe", as used by the Greeks is quite old.  We know that Herodotus was using the name in its near-modern sense, by about 430 BC.  In his examination of the world's geography, he described Europe as having an indefinite eastern border and thus was equal in size to Africa (his "Libya") and Asia, combined. (Herodotus, Book 4,45).  His "Asia" bordered Europe at the Black Sea, the Tanais, the Caspian Sea, and the Oxus (Herodotus, Book 4, 37-40).  It is to be noted that even he did not know the origin of the names of the continents, only that they were "women's names". (Herodotus, Book 4,45). 

It was in the Roman period, when the geographies gave a more modern meaning to the idea of Europe.  Sarmatia, known by Ptolemy (c. AD 150) was divided into a "European" and an "Asiatic" section, divided by the Ural Mts. and the Ural River, which is where modern geography places the division. 

The Phillipine is not a continent but a collection of islands, which are still connected to the Asian landmass. The same for Taiwan, Malaysia, Indonesia and Japan.

Picture of the 2Euro coin with the abduction of Europe:

Actually, the Indian subcontinent is believed to have been a separate land mass which collided with the Asian continent land mass, raising the Himalayas from the bottom of the ocean.

The presence of certain fauna found only in Africa and India also suggested the two land masses were once joined.

I heard about this too...but just isn't sure if it's true.