There are several threads about this here already, this one gets right to the point.
Keep in mind there are plenty of things to consider before arbitrarily applying this action. Please make sure you filter for only two name artists, and watch for special cases like Pink Floyd.
Depending on your music software, perhaps you can take advantage of the separate sorting tags such as Artistsort, Albumartistsort, Composersort, etc. so that you can leave the displayed original tags as they are now in the correct Firstname Lastname order.