[1] Genesis 11:14-15 "And Shelakh lived thirty years, and begat Eber. And Shelakh lived after he begat Eber four hundred and three years, and begat sons and daughters." See website 1.
[2] The "tower-builders" refers to the tower of Babel (see also under alpha 425, sigma 154), at which event the languages of the people were confused, giving rise to a proliferation of tongues. See Gen 11:1-9. Until the development of modern linguistics, most Christians believed that Hebrew was the pre-Babelic language, although the name of the pre-Babelic language is not given in Genesis (nor is the explanation that Eber did not work alongside the tower-builders). See Umberto Eco's The Search for the Perfect Language for a popular modern discussion.
Cf. George the Monk 52.5 ff., Malalas p. 11.15ff.
The origin of the word Hebrew might well be "descendants of Eber", or it could be via folk etymology from the root עבר "`-b-r", meaning to cross over; Abraham, first to be called עברי "`Ibri", crossed over from Ur to Canaan, though his name אברהם (Abraham) is unrelated, starting with alef, not `ayin.
(Notes supplemented by Raphael Finkel.)