>> Legendarily the O’Neills were first to claim Ireland when Heremon O’Neill lopped off his own hand and threw it ashore
Well, I’m not an O’Neill, and my family crest also has the hand...
You might want to research the matter, I’m not all that familiar with the Irish system of armorial bearing but typically when arms are “differenced” they will pick up aspects of maternal grandfather’s arms if there are no sons or the male to whom the arms belonged might even have ended up with a hyphenated surname, in England they would and in English Plantation-era Ireland they would, at least. So, you might find that you’re in some regards an O’Neill. Or, since it became so thoroughly identified with Ulster, the Red Hand may have come from their being Ulster Scots, which would be the simplest and most likely scenario.