Can I remove the labels from ICs?
Grinding or other abrasives is the only reliable method. I think I've seen machines that will do this for DIP components. 

A dedicated reverse-engineering person can probably guess the part from the pinout, surrounding circuit, and package or simply have the epoxy removed and look at the identification numbers on the die under a microscope, so it only goes so far. 

In my (somewhat) humble opinion, hiding the numbers on chips is kind of a red flag that the product is really easy to clone, has nothing proprietary in it, and is being sold for a very healthy margin, but perhaps that's just me. You won't find top tier manufacturers doing it. 

You could always incorporate one of these chips.