Name for altering a well known phrase in an obvious to convey a "new" concept?

Question

I think most people are well aware what a drag-queen is (a man dressed/acting as a woman), but I've never before today heard the phrase "drag-king"

I can however, easily arrive at the conclusion that the speaker intends to convey the concept of "a woman dressed/acting as a man"

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Back in the 70s, Richard Nixon's actions gave us "watergate" - simply the name of a group of buildings. There's no real reason why the -gate prefix should become synonymous with something scandalous, but it has and someone can say to me "iPhone 6 - bendgate!" and I arrive at the understanding that there's a scandal relating to the phone bending

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Is there a name for the process that one goes through, taking the well known, modifying it in an obvious way so that the listener can receive the new info/modification, trace enough of the original phrase to understand what it was and apply the transformation in their own mind?

Answer 1

The word "snowclone" was coined to describe precisely this kind of templatized-cliche, first promulgated by LanguageLog:

At last a suitable name has been proposed for the some-assembly-required adaptable cliché frames. I mean formulae like these (where the N, X, Y, Z are filled in to taste):

If Eskimos have N words for snow, X surely have Y words for Z.

In space, no one can hear you X.

X is the new Y.

Answer 2

He doesn’t use it in quite the same way as what you want, but in his The Devil’s Dictionary Ambrose Bierce coined a phrase that may serve, which I have emphasized in this quote:

SAW, n: A trite popular saying, or proverb. (Figurative and colloquial.) So called because it makes its way into a wooden head. Following are examples of old saws fitted with new teeth.

A penny saved is a penny to squander.
A man is known by the company that he organizes.
A bad workman quarrels with the man who calls him that.
A bird in the hand is worth what it will bring.
Better late than before anybody has invited you.
Example is better than following it.
Half a loaf is better than a whole one if there is much else.
Think twice before you speak to a friend in need.
What is worth doing is worth the trouble of asking somebody to do it.
Least said is soonest disavowed.
He laughs best who laughs least.
Speak of the Devil and he will hear about it.
Of two evils choose to be the least.
Strike while your employer has a big contract.
Where there’s a will there’s a won’t.