hmcq, your dream could mean any number of things. But let's start with a few clarifications.
1. Was your grandmother recently dead when you had this dream?
2. Was your grandmother's death wasting or quick?
3. Did you go to her funeral?
Depending on your answers to these questions could entirely change the meaning of the dream.
We shall start at the top and work our way down.
1. If your grandmother hand just recently died when you had this dream, then likely it is just another way for you to find relief from your grief. You were walking through your grandmother's house, perhaps you had fond childhood memories of the place. Did it seem as when you last saw it, or more like it was when you were a child? Either way, it was most likely a way for you to reaffirm to yourself that your grandmother had passed on. The graveyard is symbolic, it is where things go to be put to rest. That you saw your own tombstone was most likely a sign that you were putting a close to the chapter of your life that your grandmother was part of. It was nothing bad, nor foreboding. it was simply a step that you had to take in order to let go of your pain.
2. If your grandmother's death was a wasting one, it is likely that you are simply suffering from questioning your own mortality. It happens to us all, and it's quite natural to contemplate one's own death after someone dear has died.
However, was her death quick, you walking through her house may well have been a case of confusion. You weren't expecting her to die, you never had a chance to say goodbye. Walking through an area she lived in was to give you a sense of closer about her death, and the grave with your name was nothing more than a reminder that Death comes to us all and is not something to fear.
3. If you did not manage to get to her funeral, you may be feeling guilt over not being able to pay your last respects to her. This would lead to you trying to find her in a familiar place, her home is the most likely choice, and by ending up in the graveyard, you feel that you may have failed. The tombstone with your name on it a mark of what you could not do.
I hope that my answer will help you.
Yours in Spirit,