This drives me nuts, too. I have copied from another teacher and I write their names on their actual desktop with Sharpie marker. This way they are not always picking at it, I don't have to use clear tape, and I don't have to keep buying new tags when new kids show up. I can even code their names--all the kids on the Purple Team have their names written in purple and so on...

It comes off with nail polish remover. You might want to test this on your particular desks before going all out... =)