If you want to apply the names/pictures on a stock pile of previously made quilts (which I think is what you are wanting), I would use a washable glue stick or Elmers School Glue to adhere and then do a buttonhole stitch around each, through the applique, top, batting and backing. As long as your batting isn't super puffy, you should be able to accomplish on a DM. The stitches will show on the backing, but you could use a bobbin that matches your backing to make it less obvious.
As previous posters have mentioned, I would NOT iron the polyester batting at any stage of the process. Good luck.