The origin of the name Britain (british, britons, bretagne etc.)

It is interesting that in the same source you can find different answers:

http://en.wikipedia.org/wiki/Brython#Etymology

The word Brython was borrowed from the Welsh language to differentiate between this purely ethno-linguistic meaning and the word Briton. It comes from the terms Bruthin or Priteni, which were used in classical times in geographer's texts incorporating fragments of the travel writings of the ancient Greek Pytheas around 320 BC which describe the peoples of the British isles, including Ireland, as the ?????????.[1][2

http://dan.moneeek.com/content/ref/etymology/b7etym.htm

Britain - 1297, Breteyne, from O.Fr. Bretaigne, from L. Britannia, earlier Brittania, from Brittani "the Britons" (see Briton). The O.E. was Breten-lond. If there was a Celt. name for the island, it has not been recorded.
britches - 1905, from britch (1630), an old variant of breeches.
British - O.E. Bryttisc "of or relating to ancient Britons," from Bryttas "natives of ancient Britain" (see Briton). First record of British Isles is from 1621.
Briton - Anglo-Fr. Bretun, from L. Brittonem (nom. Britto, misspelled Brito in MSS) "a member of the tribe of the Britons," from *Britt-os, the Celtic name of the Celtic inhabitants of Britain and southern Scotland before the 5c. Anglo-Saxon invasion drove them into Wales, Cornwall, and a few other corners. Only in historical use after O.E. period; revived when James I was proclaimed King of Great Britain in 1604, and made official at the union of England and Scotland in 1707.

According to legend, the island's civilization was founded by a Trojan named Brutus, who fled Westward after the fall of Troy. Once on the island, he civilized the inhabitants, and then founded the city of Londonius. The island was named after him, and, with a corruption of tongues, Londonius became London and Brutus became Britain.

Of course this is all legend, & most historians don't believe it. However, it is interesting that you should mention the Lost Tribes of Israel. The Trojan Kings (from whom Brutus was said to have been decended from) were themselves put as being decended from a Dardanus, who was an early ruler. (Dardanus' grandson Troes was the man from who the Trojans got their name). Not much is known about Dardanus' true ancestory. The ancient Trojan genealogy puts him as being a son of Zeus. However, supports of the "British-Israeli" theory connect him to the "Dara" or "Darda" mentioned in the Old Testament. In the Bible, Darda is listed as just being a son of Zerah ( who was the son of Judah, who was the son of Jacob, the son of Issac, the son of Abraham, so on, so on), and not much else is said about him. They believe that the Dara/Darda of the Bible and Dardanus to be the same person, thus making the Brittons decendents of Israel (Jacob/Yaakab).

The name Britain is the most modern form of the name that has been used for thousands of years. In Welsh it is Prydain which most closely resembles the earlier celtic forms. Welsh is the direct descendant of the the celtic language used for thousands of years throughout Britain.

The Celts were not the first people in the Islands and the suggestion that the name comes from Pritani meaning painted people could refer back to the pre celtic people who were supposed to favour tattoos of animals and flowers as well as the later celts who favoured blue body paint.  There is another suggestion that it means confluence of waters. This could refer to the Islands position between the North sea and the Atlantic or it could have a religious connection as deities of water were particularly strong throughout Britain. 

There was a mass migration to North Western France from Southern Britain around  1500 years ago. The original small british community there suddenly became a distinctive British region. Thus there was a small Britain in NW France and the Larger Island of Britain. That is why we have Brittany and Great Britain or Bretagne and Grande Bretagne. As a result both Breton and Welsh are very similar celtic languages. 

The name "Britain" derives from "Bretagne" in France where tribes of the first Celts that emigrated to the British Isles came from, so the name "Great Britain" really means "Large/great Bretagne" and "Bretagne" is therefore "Smaller Britain/Bretagne", the name has nothing to do with the British Empire or any "Greatness" of any kind.