None of my grandparents are living anymore, but, I still refer to them as follows:
My mom's parents were Mamoo and Dandy. Mamoo (mom's mom) did NOT want to be called grandma (she never was! :P) so she decided on names for my older brother to call both of them. Her names chosen were Mamaloo and Sugardaddy. Well, since my brother (Ryan) couldn't say all that, Mamoo and Dandy developed and stuck. Everyone called them that, everyone except my mom. When I was younger, Mamoo would refer to Dandy as "Dandy" but as I got older, he just became "Henry". Dandy also referred to Mamoo as "Mamoo" or "My mama". Hehe, weird family, I know. :)
I never met my dad's dad, but his name was Kenneth. I just call him Kenneth if I'm talking about him. As for his mom, I always called her Grandma Bess. Her name was Bessie, and Grandma Bess is just what everyone called her! :D
So now that you know names, let me see if I can expand the weirdness in my family. Mamoo's parents were known as Granddaddy and Ninnie. I don't know the story behind these names... oh well. Dandy's mom is known as Mammow. Dandy called her Mother, Mamoo called her Ms. McCrystal, and everyone else knew her as Mammow. Grandma Bess' mom was known as Grandma Cassell (her last name). Kenneth's parents were known as Mud and Faf.
As for anyone not mentioned, it's probably because I don't have the slightest idea what their name was or what they were called. Oops. And most of these names were known by everyone, not just the grandkids. My great-grandparents were still referred to as "granddaddy" and so forth just because that's what my parents called them; and many people called my grandparents by the names I called them, just because that's how it stuck. :)
EDIT: I just found out a few names that I was unsure of. My dad's mom's dad's name was Granddad Cassell - he was married to Grandma Cassell. My mom's dad's dad's name was Granddaddy - he was married to Mammow more than once. The other man married to Mammow was known as Bud.