That's what intrigues me. When people put fake logos on cheap copies, it's clearly because they want to pretend their cheapo is the real thing. But when someone, like yourself, produces a genuinely beautiful, top quality instrument in which hours of labour and love have been invested, I'm honestly puzzled as to why you wouldn't want to stamp it with your own imprint and say to the world, look, I made this myself!
If I saw your guitar, with your own name (or whatever you wanted) on the headstock, I would certainly want to take a closer look. As it is, unless you told me differently, I'd simply look at it and think, "Hmmm... nice Strat", and pass on without another thought.
So, please understand, I'm not saying you shouldn't do it if you want to, just asking, out of genuine interest, why you would want to.