I agree that identifying yourself with the label rationality … But it still seems useful to have some sort of terminology to talk about clear thinking, and I can't think of a better candidate term than rationality.

‘Rationality’ is a perfectly fine term to talk about clear thinking, but that is quite a different matter to using 'rationalist' or any other term as a label to identify with.

I must say that I can't help but find it odd that you link to "Keep Your Identity Small" in discussing this problem. Did you read the footnotes? Graham lists that which we would call rationality as one of the few things you should keep in your identity:

He doesn’t quite say it’s a label you should keep in your identity, he lists it as an example of something that might be good to keep in your personal identity. I think that the argument he outlines in the essay applies to what’s in that footnote: that it’d be better to just want to “[follow] evidence wherever it leads”, than to identify too strongly as a scientist.