My father's aunt Jane Alcock was born in Kinsale, Cork in 1864. While she is obviously not your ancestor, it is a family name. The earliest record of the Alcock family in Ireland that I have found is their arrival in Waterford among the Cromwellian Adventurers in the 17th century. My branch has been in Cork since at least the late 18th century.
Great aunt Jane was the daughter of William Alcock and Esther (or Hester) Driscoll, who married about 1860 and had children Jane, Honora, Margaret, William Francis and Jeremiah Joseph. I believe her grandfather was also William Alcock, who married Jane Pratt in 1823 in Kinsale.
I'd appreciate anything you know about the Waterford Alcocks, especially if these names suggest a connection.