Hayes and Griffin

I am trying to find information on my great grandfather John J Hayes. His death certificate stated that he was born in December 1862 to Richard Hayes and Mary Griffin. After several years of looking for him, I have found a John Hayes born to John Hayes and Mary Griffin in 1859. John immigrated to New York around 1880. He married Mary Fitzgerald in 1886. I am learning that dates are not always accurate. Is it possible that first names are not either? Any help would be very much appreciated.

Thank you.