No, you cannot change your headstone design after it has been laser engraved. A design has been crafted to your exact specifications including the color, size, and type of monument you have selected. If details such as your name and birth date have already been engraved onto the monument there is absolutely no way it can be changed.
When a headstone design has been selected and laser engraved, the minerals in the stone are melted and burned away. There is no way to fill or camouflage the engraving once it has been etched. It is very important that you are happy with the headstone design after you have given permission to proceed with engraving. If you have any questions regarding what the design will look like before it is engraved, request a proof. A monument dealer should provide you with a design proof that shows your name and dates in the chosen fonts as well as the monument style and color of the gravestone you selected.
Monument companies should be able to show you examples of work on particular types of stone as well as examples of different designs and lettering. Ask if you can see any photos or examples of a particular design or font if you are considered getting it engraved on your headstone. Most monument companies should be able to give you some kind of example of their work from previous clients.
A design proof is sent to you for approval before the headstone engraved. That is the time to raise any questions or ask any friends for opinions. Once the proof is signed and sent back to the dealer, you have given your written consent to proceed with engraving.
It is very important that you have considered all your options when your designing a headstone because engraving is permanent and once you have given permission to proceed with the design it cannot be changed.