Is it possible to reuse an old headstone? Can we have it engraved for someone else?

Answer 1

If you own the headstone you can do what you want with it. Take it to stonemason and ask them.

Answer 2

You have given a whole new meaning to the word, "frugal."

You can have a stone cutter etch away the existing name and information and replace it with something else, but why would you want to? Someone bought that headstone to mark the grave of some person. Would you remove such a memorial? Is that person no longer worthy of being remembered?