I don't take finished projects to the embroiderer any more. If they mess up, your whole project is ruined. Lately, I just bring an oversized piece of the fabric I want embroidered & then when I get it back I cut it down to size & piece it and then quilt.
At the latest, you could bring your pieced stocking "quilt top". I think it would be tricky to do a nice job with the embroidery if it's already quilted (and I would imagine the stabilizer would then be visible on the top inside of the stocking. Make sure to discuss the cost of the embroidery with your friend in advance. I typically pay around $8-10 per name where I live.