The name is as an acronym of the “American Committee for the Relief of Ireland”. It dates back to the 1920s to the Troubles of those times (1920-1922).
"Read letter dated 2nd inst, from the Hon Secretary, Irish White Cross, intimating that their Committee propose to erect forty-two working class dwellings in new street off Beechmount Avenue and requesting that the street be named "Ancomri" Street and it was resolved that the request be complied with". (12th September 1922)