You're a little incorrect, but understandably so; the term "rationalist" refers to "rational thinking", which in turn is a term snatched from Daniel Kahneman's book "Thinking Fast and Slow", which summarizes a great deal of revolutionary findings in the fields of cognitive psychology.
However, I agree- they should have picked another name. "Rationalism" already exists. Furthermore, it's an arrogant name to have- calling your group "rational" implies that anyone who's not in your group is not rational.
I don't understand. Rationalism in the philosophy world goes back to Descartes. I think that's when it was an explicit school of thought, perhaps a hundred years later at the most. I also rather like the philosophy distinction between rationalism and empricism (strangely enough, the online 'rationalists' seem to be empiricists) since it's a division between traditions with differing but obviously valuable approaches to how people know things - rather than one side simply taking the name to claim some kind of high ground. The name actually illustrates something distinctive about each group's thought.
However, I agree- they should have picked another name. "Rationalism" already exists. Furthermore, it's an arrogant name to have- calling your group "rational" implies that anyone who's not in your group is not rational.