As far as I know, Eurasian Eyes is because of his spouse, Pulse is because he lost feeling in his hands on the FA, and Driven was because it required so much effort to bump another letter grade.
Rush to my knowledge had nothing to do with those three, but there may be others.
Pulse is actually the Pink Floyd Division Bell live tour and the direct start to Division Bell. Losing feeling in the hands was probably secondary.
As for the Rush route names what do Fly By Night, A Show of Hands, Permanent Waves and Caress of Steel (to name four JS routes) all have in common?