Hi,
It would be great if you could post the picture of the coin slab/ label.
Often times, slabbed coins contain labels which contain the name of the person who submitted the coin for grading as part of their personal collection. I've seen many such slabbed coin labels bearing the name of the coin collection's owner. As I'm yet to submit a coin for grading myself, I can't discuss on whether one is given an option to include one's name/collection in the label, when submitting the coin to a grading agency.
regards,
Soubhik.