Why are Jews called Sephardim and Ashkenazim?

I should clarify the question: the Hebrew words for the countries of Spain, France, and Germany, were for centuries, Sepharad, Tzarftath, and Ashkenaz, respectively, although in the modern era Germany has been reverted to Germania (with a hard G).

The problem: those three Hebrew words are all of Biblical origin and refer to places in and around the Holy Land, and, more importantly, the traditional names for those European countries are ancient and already appear in Mishnaic and Talmudic sources. Aspamya and Germania appear in the Mishnayoth! (Although in the Yerushalmi, Germany is already associated with Ashkenaz.)

Why would it be that these well-known countries received new, transplanted Hebrew names? Tzarfat is in what is now Lebanon, and Elijah the prophet lived there. Why would France become Tzarfat?

The answer came to me about two years as I was reflecting about the interesting distinctions that are maintained between various Hasidic sects. No Satmar or Vishnitzer Hasisdm ever set foot in Satmar or Vishnitz. They, like my grandfather was want to say, merely took the name from some antisemitic town in Europe. Think New Square. There was old Square in Hungary, and now the entire community is in America. Yet, it is a critical part of their identity. The same may be true for all of the Ashkenazim: They, like the Jews who lived in ancient Palestinian Tzarfath and Sepaharad, called their new European homes by the names of their original homes, and over the course of time it was forgotten where they had originated.