I have done it both ways. Sometimes I quilt first, then handstitch the label on. Other times I have pieced the label in (a fancier embroidered one) and do the quilting right over it.
I have also done it both ways (before and after quilting) If it is after, it really must be hand appliqued, to prevent showing through on the front. If it is before, careful placement and basting is the key. Often it is best for the LA quilter to baste it through all the layers to see exactly where it is in relation to the backing as it is loaded on the frame. If you baste it yourself to just the backing fabric, give the LA quilter specific instructions on where you want the label to end up (bottom right corner, centered at top, etc.) In either case, I always make my labels with interfacing for stability and fully finished edges.