If you're going to do this because you don't want to be a walking advertisement, then you need to carry this through all aspects of your life.
Don't stop at the camera. If you have a car, you need to remove its identifying logos. Same with your television and other electronics, your clothes, all food in your house and all items that can be identified by people who might be in your home. This includes film, because no one has the right to know what film you're loading into the camera. Remember to not label any of your photographic chemicals, because you shouldn't be wasting your time promoting a manufacturer's product.
Just make sure that you're consistent in what you do.