I think you'd agree that pitch dynamic stability seems more
intuitive.
I'll agree that it is the aviation-industry-standard term.
But I continue to advocate using "damping" rather than "dynamic stability"
in all cases.
Also, in this particular case Brian described, rather than calling it
"pitch-axis damping", an even better term would be "angle-of-attack
damping". An ordinary airplane in flight has
gobs of AoA stability,
marginal AoA damping, and
very little (ideally zero) sensitivity to pitch except via AoA;
i.e. AoA is a "sufficient statistic":
if you know the AoA you don't need to know the pitch.