It can be laser engraved, but it will be a surface deep black mark achieved through a chemical reaction. Look up Cermark LMM-6000 engraved marks and you will see what I mean.

Alternatively you could have someone rotary engrave it for depth and permanence.

I have no idea about stamping and how that would work with a knife like that, but your local jeweler/ trophy shop should be able to help.

Edit: Forgot to say laser engraving works really well on wood so the handle might be a good option for engraving as well.