Like mic-pa I have found that if I machine stitch on the back with the bobbin thread ( now on the front of the quilt) the same color as the quilting thread, it isn't noticeable at all from the front.

I sew my label into the binding on two sides and hand sew the other. Sometimes square label sometimes triangle.
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I think you put your label where you want it. My labels are put on like AZ Jane's front or back depends what is on the label. This is one I put on our granddaughter's wedding quilt. The quilt is black, silver and navy blue, the wedding colors.