It’s called Keep a Word - Delete a Word.
Example: I post the first two words.
Couch Potato
the next person quotes me and changes one of the words:
Potato Pancake
The next person quotes that and changes it:
Pancake Syrup
You always keep one of the two words - and you change the other one so that the two words still comprise a common phrase.
So I’ll start.
Final Analysis