Everything we think we know about the goddess Ériu (and Irish mythology in general) was written down within the past 1000 years by Christian monks. They purported to be recording the oral mythology of the Irish people, but it’s hard to say how much of it was a faithful transcription and how much was invented/reworked by the monks to fit into a Christian/Greco-Roman worldview.
The etymological root of Ireland as a place name ultimately derives from ancient Greek sources, which obviously predate such mythology by over 1000 years.
The name Ériu has been derived from reconstructed Archaic Irish *Īweriū, which is related to the ethnic name Iverni. The University of Wales derives this from Proto-Celtic *Φīwerjon- (nominative singular Φīwerjō). This is further derived from Proto-Indo-European *piHwerjon- (“fertile land” or “land of abundance”), from the adjective *piHwer- “fat” (cognate with Ancient Greek píeira and Sanskrit pīvara, “fat, full, abounding”).
The Archaic Irish form was borrowed into Ancient Greek as Ἰέρνη Iernē and Ἰουερνία Iouernia, and into Latin Hibernia.
So, even ignoring the fact that a mythical goddess is not equivalent to a human woman, Ireland wasn’t named after a goddess either.
Everything we think we know about the goddess Ériu (and Irish mythology in general) was written down within the past 1000 years by Christian monks. They purported to be recording the oral mythology of the Irish people, but it’s hard to say how much of it was a faithful transcription and how much was invented/reworked by the monks to fit into a Christian/Greco-Roman worldview.
The etymological root of Ireland as a place name ultimately derives from ancient Greek sources, which obviously predate such mythology by over 1000 years.
So, even ignoring the fact that a mythical goddess is not equivalent to a human woman, Ireland wasn’t named after a goddess either.