Suppose that instead of following a style guide (like the Associated Press Stylebook) that called for putting book, movie, and TV show titles in quotation marks, you were following one (like The Chicago Manual of Style) that recommended putting them in italics. And suppose that you had to punctuate and style the following sentence for maximum coherence, without changing a word:
George Lucas said, "I've decided to name the sequel to Star Wars The Empire Strikes Back."
First, Chicago would require you to italicize the two movie titles, which would leave you with this:
George Lucas said, "I've decided to name the sequel to Star Wars The Empire Strikes Back."
To me, that string of italics looks like a single run-on title, and I could easily see adding a comma in hopes of helping readers find the break between the contiguous names:
George Lucas said, "I've decided to name the sequel to Star Wars, The Empire Strikes Back.
I might even argue that the comma represents a visual signal that important elements had dropped out of the original idea informing the sentence, which was something along these lines:
George Lucas said, "I've decided to name the sequel to Star Wars, [and the name I've chosen is] The Empire Strikes Back.
In any case, you can hardly deny that the comma helps readers identify the seam between the two unfortunately adjacent titles—and the point of punctuation, I think, is to improve readability by providing clarifying services such as that one.
Now consider the same sentence done in AP style, where quotation marks, not italics, are needed:
George Lucas said, "I've decided to name the sequel to 'Star Wars' 'The Empire Strikes Back.'"
The comma is no longer necessary to signal the break between titles, because the two sets of quotation marks do that job. But does that mean that including a comma after "Wars" constitutes an error? I don't think so. I think the decision to include or to omit the comma here is a judgment call that ought to be left up to the author or transcriber/editor.
Note that we're talking here about how to handle the content of a sentence that is essentially a found object. Most style guides don't worry about issues like this one because, if a sentence looks too weird, it's a clear sign that the author should rework it or paraphrase it so that it doesn't stop readers in their tracks. But if you're transcribing a direct quotation, you don't have any wiggle room: you just have to do your best to make the meaning clear. To me, both
"They just renamed 'The Kelly File' 'Becky with the good hair.'"
and
"They just renamed 'The Kelly File,' 'Becky with the good hair.'"
are satisfactory on that count, and therefore neither is wrong. Harder to defend is the transcriber's decision to treat 'Becky with the good hair' as a sentence-case phrase instead of as a title ('Becky with [or With] the Good Hair'), which (after all) is what the joke claims it to be.
