It was not moved. Simply it is- in bout cases- exomym.

Peoples of that Caucasian region were known to ancient Greeks as Albanoi, thus the land was named Abania. How that name came to be, is not entirely clear as Persian and Armenian names are rather dissimilar (Arran and Aluank respectively). However region was know for being home of many different tribes, so its most likely deriving from on of them (ancient geography ridden with such cases).

Albanians in Europe were first mentioned by Ptolemy as one of Illyrian tribes. Nothing else is known about them until 11th century, then Albanians revolted against Byzantine empire. Albanians themselves call they land Shqipëria, but most of European languages adopted classical term (just like Iran was called Persia until 1930's).

It is hard to say if these names are related (albeit that is unlikely) or what are exact etymology of them, because we really don't know how these ancient peoples called themselves or who supplied Ptolemy (and others) with these names- all we know that Greeks called them so.

P.S. A bit more info about Caucasian Albania.

http://www.iranicaonline.org/articles/arran-a-region http://www.iranicaonline.org/articles/albania-iranian-aran-arm

The Albanians don't call themselves "Albanians." Their word for themselves is "Shqiptarët," and their name for their nation is "Shqipëri."

This isn't uncommon, really. The Koreans don't call themselves Koreans. That name is derived from the name of one dynasty, the Goguryeo. Their name for themselves is "Han," and their country is "The Han Republic." The Basques call themselves "Euskaldunak," or "Those Who Speak Euskara," (their name for their language). Hell, the Germans don't call themselves "Germans." They're the Deutsche, living in Deutschland, speaking Deutsch.

Perhaps I'm mistaken but wasn't there another region called Iberia also in the caucus area? Was there any connection to the peninsula that houses Spain and Portugal?