We only use gift bags if there is no time to wrap, since I love to wrap gifts even more than I like opening them. It always reminds me of Christmas at Grandma Helen's (the best Christmases of my life).
My family has a tradition of one box under the tree is wrapped especially nice, ribbons, bows, foofoo, etc. that gift is never given a label. It is part of our Christmas season to guess who it is for, what it might be, "I hope it is....", "I hope it is mine", etc. Christmas morning, it is the last gift under the tree, and only after all other gifts are opened and oooed and ahhhhed over, only then is the secret told, and the lucky recipient gets to open it after everyone has a last guess at what it is. Yes, you may take our tradition and adapt it to your own celebration. Merry Christmas all!