Our family exchanges many Amazon wrapped gifts. The bags are fantastic for reuse, and to make it even easier, the tag loops can be reused as well by removing the old tag and looping a new tag in (here is a short video). Even easier, fold the little tag Amazon sends with the gift, and punch a hole in. The paper is flexible enough to thread through the loop to attach the tag.

Yes, you could also glue or tape the preprinted tag onto the old tag. I have also been known to make a hand written new tag, but now I have another option to solve the labeling gifts issue. I like choices.