Is there a name for change in attitude with respect to time?
The components of attitude vector are called:


yaw (or heading) is the angle of longitudinal (x) axis in horizontal plane,
pitch is angle of longitudinal (x) axis from the horizontal and
roll is angle of lateral (y) axis from the intersection of the yz (orthogonal to longitudinal axis) plane with horizontal.


And their derivatives are usually yaw-rate, pitch-rate and roll-rate. Second derivative names probably vary.

Regarding coordinate system, the first axis, called x, is always longitudinal and positive direction is forward. The second axis, called y, is usually lateral one, but positive direction is right in some systems and left in others. And z completes a right-handed coordinate system (so your vector products work the usual way), so z down if y points right.

Edit: I thought u,v,w is sometimes used as alias for the axis, but actually they are usually rather used for the velocity vector components.