Fitting for this thread, the chain was actually named for its McDonald brother founders, who were the American sons of Irish immigrants:
https://en.wikipedia.org/wiki/Richard_and_Maurice_McDonald
(I believe “McDonald” is the Irish spelling and “MacDonald” would be the Scottish spelling.)
Both Irish and Scottish use “Mc” and “Mac” variants actually. The Gaelic word “mac” means “son”; Viking and Saxon influence is why you have both “McDonald” and “Donaldson” in use in the British Isles.