To recap this, a common refrain from science illiterates is that the term "climate change" has been more preferentially used in the last (insert time frame here) ever since "global warming" turned out to be (insert false claim here). e.g.
"They used to say it was global warming until the globe stopped warming and now they call it climate change"
Searching through Google-indexed books and Google Scholar shows this claim isn't true. But what if we search the U.S. Congress? Capitolwords.org has indexed Congressional speeches since 1996 and thus it provides 17.66 years of data on whether "climate change" is now discussed whereas "global warming" used to be.
Orange is "climate change", red is "global warming". Both have been pretty highly discussed since 1997, with a peak of activity during the summer of 2008.
There are a few times when "climate change" is discussed a lot in Congress without "global warming" also being mentioned, namely in 2002 and 2013. The 2002 trend appears to have been a blip, who knows about the 2013 trend.