What is the possessive of McDonald's?

This makes the quite understandable mistake of assuming that the apostrophe in an English possessive isn’t there as part of a contraction. It is, of course, it’s just that we’ve forgotten what the original inflected form was that we are contracting.

I know what the origin is. It’s a matter of what its function is now. No one today would say “McDonald his hamburgers.”

This discussion suggests not.

This suggests so.

For Christ his sake. Did you want a whole detailed explanation of the evolution of the use the apostrophe to indicate possession? As the in the thread indicates, the origin is debatable, and Quinion (my cite) contradicts Millward (cited in the thread) to some extent. While in either case the use of the apostrophe is based on the mistaken idea that the original possessive “s” represented an abbreviation of “his,” at least according to Quinion that abbreviation is the basis for the widespread use of the apostrophe (even though mistakenly).