Re: is it wise?
You could possibly get away with it, but if you decide to sell it, you would have to get a little plate soldered over it that matches the sax's paint job. Soldering can leave a mark similar to a scratch.
You could also have your name engraved inside the bell, jsut far down enough that nobody will notice during performances. Or maybe you could have it engraved on the side of the body of the sax that faces you when you play.