Oichrig is the Gaelic name that corresponds with Effie.
Like Seumas and James, or Seoras and George, or Mairead and Margaret.
For many years it was frowned on to register your child with a Gaelic name, and parents registered the child with the English form of the name and then actually addressed them by the Gaelic form. Even the names that aren't translated mostly have English equivalents, such as Calum being Malcolm and Iain being John and Catriona being Catherine. My own name is often given as Sarah, although my birth certificate actually says Morag. (My grandmother was Sarah though.) (ETA: I should clarify that nobody calls me Sarah, I meant that in English-to-Gaelic translations you'll often find Sarah turning into Morag.)
My father's registered name was James, but as a boy he was always called Seumas, and of course addressed directly as a Sheumais. This morphed into the name he always had within our family - Hamish, which is what Sheumais sounds like if you write it in English.
In Gaelic-speaking parts of Scotland it is still quite common to address people by the English form of their name if you are speaking in English, and by the Gaelic form if you are speaking in Gaelic.