A long, long, long time ago (all the way back in 2008, which might as well be a century in Internet years) we started a quest to find Mc- and Mac-Jews. In the century (decade) since, we've discovered a bunch. Most got the goyishe surname through their goyishe father, while the Jewishness came from the mother's side. (Traditionalists like it that way.)
This brings us to Al McCoy, World Middleweight Champion from 1914 to 1917, the first ever southpaw to hold a world boxing title. 100% Jewish, no need to limit to matrilineal: his father was a kosher butcher. Does that mean there was a kosher butcher with a name of McCoy?
Absolutely not. Al McCoy was really Alexander Rudolph, who changed his name so that his religious parents didn't find out that he was a boxer.
Here we ask you, Jewish parents: what fate is worse for your offspring... becoming a boxer or changing their name to the ultra-goyishe McCoy?