How can I erase the logo from the headstock? Will I have to sand away the finish or something? How can I insert my own custom logo and how do I fix any subsequent damage?
Dear God, do you actually answer prayers?

Yes, but only in a way indistinguishable from random luck or the result of your own efforts.
depends some logos are inlayed and some are painted on
either way youll have to do some sanding to remove the finish
You could paint over it if you don't want to sand it off or if it's an inlay.

I'd say primer it first, then paint the headstock the color you like and then put your own logo or make your logo big enough or the right shape to cover the original logo.
Imagination is more important than knowledge...
It is a miracle that curiosity survives formal education.
- Albert Einstein -