First came John Guare's play Six Degrees of Separation, which was later turned into a film. It was about the web of interconnections that binds all of humanity together.
Later came the well known trivia game Six Degrees of Kevin Bacon, which does for actors what Guare's creation did for the rest of us. But lately more people understand the idea behind "Six Degrees of Separation" through the Kevin Bacon game. The game has supplanted the inspiration for it.
Now, it seems obvious to me (though I could be wrong), that Kevin Bacon was chosen at least in part because his name metrically and phonetically rhymes with "Separation" (at least the vowels do). "Six Degrees of Jack Nicholson" or "Six Degrees of Lord Laurence Olivier" wouldn't have scanned as well (or at all).
So here's my question: Is there a term that succinctly represents the transformation of a word or phrase through assonance or rhyme into another word or phrase of similar meaning, but in which the latter version becomes more well known than the original? Failing that, perhaps this falls under a larger category of word or phrase substitution. I've been trying to think of more examples, but I can't at the moment, though I am sure they exist.
N.B. I am not asking about any "real" reason Kevin Bacon was chosen, about the origin of the game, its history or rules or any of that. That information is covered extensively elsewhere. I'm only interested in the term for such a transformation, if one exists.
Best Answer
Note: There is some contention as to the applicability of this answer. I am directly addressing this portion of the original question:
The best term I found was meme:
The key here is the mutation. In the case of your example, there is a rhyming/assonant mutation and Six Degrees of Separation became Six Degrees of Kevin Bacon.
There are plenty of other examples of meme evolution; many of them thrive in chain emails or on Facebook. The one example that really stuck with me, however, was the "25 Random Things About Me" chain that hit in 2009. The reason I remember it well was because of this article in Slate magazine that compared the fad to a virus:
Studying the idea of Six Degrees of Kevin Bacon outlasting its predecessor would fit the scope of measuring popularity and catchiness. Much like pictures of Keanu Reeves on a bench or Xzibit's goofy phraseology, concepts morph until they stick in the popular consciousness. Naturally, rhyming makes a logical next step in the evolution of a phrase. So would swapping out a generic word (separation) for a specific cultural, er, icon (Kevin Bacon).
Of note, Wikipedia even calls the it a meme:
While a more specific term may be found, meme certainly works as a backup umbrella term.
A more specific alternative: The Weird Al Effect
This is, again, not a specific match based on rhyming but the idea of a variation becoming more popular than its original again matches. The effect also carries a heavy implication that the child term survives the parent term's fade into obscurity.