I have tried to use the label tool and allow the auto label with the component name. Wht ends up really happening is the label displays child components of the component. So if you have nested components and the top level is the main components (and obviously structured that way for a reason) then one would expect the labeler to label per the highest level component the user is selecting and not the sub components or nested components. The child components could always be labeled if the parent component was drilled into.
So as it stands, both sketchup and Layout label tool do not really label the component selected but reads down the hierarchy selects the component it thinks you are pouting to and completely ignoring the parent that you are really pointing to.