This surname should originate from the Fitzgerald dynasty in Ireland, but the Fitzgerald dynasty is not Irish, but Norman, and Norman is the descendant of Viking pirates. But their integration with the local Gaelic-speaking Irish is so close that they are considered "more Irish than the Irish".
The Mo Chuisle in the movie is Irish Gaelic, which is in line with Fitzgerald's Irish dynasty background. The screenwriter chose the name Fitzgerald, perhaps with careful consideration.
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