The viewport name can be anything, you can change it in the Viewport Properties panel (and save the drawing afterwards). And as @Zen said, there is no correlation with the camera orientation. You can change it to a perspective view, and the name will still be Top.
If you need to look at both orientations Left and Right a lot, it makes sense to either change one of the four available viewports permanently by changing both name (Viewport Properties) and orientation (Set View).
Another way is to use NewFloatingViewport. You have to find out yourself how that works for you, I never tried it sofar.
Max.
Edit: It seems this is not the normal behaviour, and may be changed soon. See the thread that @wim referred to.