>> Called by the natives "Erin," i.e. Eri-innis, or Iar-innis (west island).

Erin is an anglicized form of the Irish word Eireann, which is the genitive version of Eire, the Irish name for Ireland. You see the Irish version in the names of present-day national organizations like Iarnrod Eireann (the Irish railway company) or Bord Luthcleas na hEireann (Irish Athletic Board). Erin is little-used by anyone these days, except perhaps sentimental Irish-American parents (viz. Colleen, Shannon) or aficionados of bad 19th Century poetry.