The usage when applied to names precedes McDonalds and frequently isn't associated with the chain. Instead, "Mc-" is a common form for making generic names, derived from Scottish and Irish patronyms.
The Oxford English Dictionary lists this as its first entry for "Mc-, comb. form:"
Prefixed chiefly to nouns to create mock names denoting a person who (or occasionally thing that) is considered an exemplar or personification of the specified class, interest, association, etc.
The first example is from the 1940s:
1948, San Francisco Call-Bull. 21 Dec. 20/1: "Dear McSanta: All I want is a few extra college credits."
So "Somebody McSomebody" is a generic person, perhaps to the point of mocking.