Our grosgrain wedding gown labels come with a “pinked” (zig-zagged) edge to prevent fraying. Most people tuck in these edges and apply it to the gown as shown.
Once pinned in location, you can press the edge with your finger or a warm (not hot) iron before doing a whip stitch to sew it into place. In doing the stitching, take a little bite of the lining fabric of the dress (being careful not to catch the front dress fabric in the stitch) and then catch a bite of the label itself. Do this along the edge of the label on both sides. It does not take a lot of stitches to hold the label firmly in place.