Art director J. McMillan Johnson (most commonly credited form according to the Credit Lookup Tool), also credited as Joseph McMillan Johnson and as Joseph MacMillan Johnson (I read that name in the credits of Hitchcock's Rear Window).
Is McMillan a Middle Name or the first part of a double barreled Last Name?
I couldn't find any source on the net to prove either the former or the latter.
I can just say that McMillan is a common surname of Scottish origin (1 in 6250 families; popularity rank in the U.S.: #757) , and that he married a McConnelly!, so I would be inclined to think that "McMillan Johnson" is his Last Name, but I can bring no definitive proof of that.  On the other hand, there is no proof that McMillan is his Middle Name either

Quoting skipnet50:

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Treat it as a middle name unless you can provide documentation that it is not, nothing to sweat about or even worry about. But don't make an assumption.

Skip

Where in the Rules is it said that we should assume that a name is a Middle Name unless we can provide documentation that it is not? I cannot provide a definitive proof, but McMillan is generally used as a Last Name. On the other hand, there is no proof that it is a Middle Name either, and I can't find any "When in doubt, default to Middle Name" rule. 

Just to confuse the matter further, it is known is this country for mothers to use their maiden name as a child's middle name! So McMillan could have been his mother's maiden name, but is still a middle name.

Quoting tweeter:

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Book excerpt where he's referred to as Johnson
Wikipedia - referring to him as Johnson

A "greenie" to you! 
Usually I am good at finding information on the net, but this time I didn't think of Google Books. Thanks!

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Also, to echo Northbloke, the same is not uncommon in the states. My brother's middle name is my mother maiden name.  My best friends son's middle name is his mom's maiden as well.

Good point as well.