That guest is full of it.
Martin is not a uniquely Spanish name at all. He was a very popular saint throughout all of Christendom (well, the western part of it) and I dare say many Irish bore the name well before the Armada.
The Armada did NOT primarily land in Galway Bay.
From Hardiman's History of Galway
"The year 1588 was rendered memorable for the destruction of the celebrated Spanish Armada. One of the ships which composed this ill-fated fleet was wrecked in the bay of Galway, and upwards of seventy of the crew perished. Several other vessels were lost along the coast; and such of the Spaniards as escaped the waves, were cruelly butchered by order of the lord deputy, Sir William Fitz-Williams, who, finding, or pretending to find, fault with the alleged lenity of Sir Richard Bingham, the president ot the province, commissioned Robert Fowle, deputy marshal, who dislodged these unfortunate men from their hiding-places, and in a summary manner executed about two hundred of them, which so terrified the remainder, that, though sick and half-famished, they chose sooner to trust to their shattered barks, and the mercy of the waves, than to their more merciless enemies, in consequence of which multitudes of them perished."
A typical galleon carried roughly 200-400 men (and mostly on the conservative side of the estimate), the one directly in the Bay lost 70 men there alone. We do not know how many more had already died from sickness or injuries. Presumably the survivors were massacred and the wealthy ransomed. Those along the coast fared even worse. How one could conclude the Armada had a significant effect on the ethnic makeup of Ireland, is beyond me.
Anne Miler could say she was Black Irish, but how that proves an Armada link, I fail to see.