[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 web address 1.
[2] The "tower-builders" refers to the tower of Babel (see also under alpha 425, sigma 154), where the languages of the people were confused, giving rise to a proliferation of tongues; see Genesis 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, Chronicon 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 ʿ-b-r, meaning to cross over; Abraham, first to be called עברי ʿiḇrī, crossed over from Ur to Canaan, though his name אברהם ʾaḇraham is unrelated, starting with alef, not ʿayin.