The name berber came after the fall of Roman Empire.

The name Berber appeared for the first time after the end of the Roman Empire.^[3] The use of the term Berber spread in the period following the arrival of the Vandals during their major invasions. A history by a Roman consul in Africa made the first reference of the term "barbarian" to describe Numidia. Muslim historians, some time after, also mentioned the Berbers.^[4] The English term was introduced in the 19th century, replacing the earlier Barbary, a loan from Arabic. Its ultimate etymological identity with barbarian is uncertain, but the Arabic word has clearly been treated as identical with Latin barbaria, Byzantine Greek βαρβαρία "land of barbarians" since the Middle Ages.
For the historian Abraham Isaac Laredo^[5] the name Amazigh could be derived from the name of the ancestor Mezeg which is the translation of biblical ancestor Dedan son of Sheba in the Targoum. According to Leo Africanus, Amazigh meant "free men", though this has been disputed, because there is no root of M-Z-Gh meaning "free" in modern Berber languages. It also has a cognate in the Tuareg word "amajegh", meaning "noble".^[6][7] This term is common in Morocco, especially among Central-Upper-North Morocco Tamazight and Central-Upper-North-South Morocco Sous Tamazight speakers in 1980,^[8] but elsewhere within the Berber homeland a local, more particular term, such as Kabyle or Chaoui, is more often used instead in Algeria.^[9]
The Egyptians, Greeks, Romans, and Byzantines mentioned various tribes with similar names living in Greater "Libya" (North Africa) in the areas where Berbers were later found. Later tribal names differ from the classical sources, but are probably still related to the modern Amazigh. The Meshwesh tribe among them represents the first thus identified from the field. Scholars believe it would be the same tribe called a few centuries after in Greek Mazyes by Hektaios and Maxyes by Herodotus, while it was called after that the "Mazaces" and "Mazax" in Latin sources, and related to the later Massylii and Masaesyli. All those names are similar and perhaps foreign renditions to the name used by the Berbers in general for themselves, Imazighen.


http://en.wikipedia.org/wiki/Berber_people#Name