I think a general rule of thumb is to figure out when your ancestors went to Ireland. If they were connected with the Norman invasion of Ireland where the rulers went native, they're generally considered Irish (the name Fitzgerald indicates that you were the bastard son of Gerald of Wales, who helped lead the Norman invasion, but Fitzgerald is still considered an Irish name). However, if you're related to the Scottish Presbyterians who were transplanted to the Ulster area after Cromwell's invasion, you're generally considered Scots-Irish. I don't think name alone is an indicator, though.
Not that it really matters beyond curiosity.