My father came from Rathdrum, Co.Wicklow. His name was spelt Errity, but somehow it gained a t when he came to England in the 1930s. We have relatives in Wicklow, Dublin Area, and other parts of Ireland. I live in Sussex, though I was born in Middlesex. It seems that Errity/Erritty is related to a very old Irish name MacOireachtaigh or MagOireachtaigh which means 'son of an assembly member', and is related to Geraghty (a more common name). There are Erritys in Canada, USA and Australia.
I haven't done much work on this, but I'm sure someone has!