That's one version. Some Gaelic scholars believe an alternate translation for Kennedy is "ugly headed". Having watched Teddy age over the last 40 years, I tend to believe the latter.
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The surname Kennedy is very common in Ayrshire (SW Scotland), which is where many of the Protestant settlers in Ireland came from. So a Kennedy in the US is often of Scots-Irish ancestry. I don’t know if further back in the Middle Ages the Scottish Kennedy family and the Irish Kennedy family were related.