I call my grandmother Mamaw (what can I say? I live in the mountains of North Carolina.) My son calls my Mom Nonna. My Step-dad is Italian, so it fits for her.
My maternal grandmother was Gammy, my paternal grandmother was Dada, pronounced DAY-da, from her name, Ada.
My wife became a grandmother at 36. Ten grandkids later she is Samma (from Samantha) to all of them.
Parenthetically, I am Granpa Doug to most of the kids. For a whiile in each case I was Granpa Duck when they were having trouble distinguishing the hard G from a K. I was kind of disappointed when they each grew out of it. However, one set of grandsons, 7 and 10, now call me Biddyguck for fun, which is how one of their cousins mangled Granpa Doug for a while.
My maternal grandmother was “Nannie.”
My paternal grandmother was “Grandma [First Name].”
My paternal step-grandparents were “Grandma/Grandpa [Last Name].”
My maternal step-grandparents were “Pappy” and “[First Name].”
I called my grandmothers “Oma Lastname”, never by their first names. I think I grew up thinking that ‘Oma’ really was their first name. 
Same goes for the Opas. My family’s Indonesian, so I’m not really surprised that we went with ‘Oma’ given Indonesia used to be a Dutch colony.
…come to think of it, I really can’t remember any of their firstnames. Except for my maternal grandmother and that’s because I have her address.
Dead. /rimshot
Never knew a Grandmother, but my Mother’s dad was Grampa Swede and my Father’s dad was Poppy.
I may have posted this before.
My dad’s parents were Masy and Pasy (pronounced Mah-zee and Pah-zee), named by me as soon as I could talk, and called that by virtually everyone who knew them thereafter. At my Masy’s funeral, there were people who didn’t know her real name, but knew she was Masy.
My other grandparents were more mundanely called Grammie Rand and Grampie Rand.
My mother-in-law is Mimi to her grandchildren.
Both grandmothers died before I was born. However, my mom was a grandmother when I was born, and she was “Nana” to one set of grandkids, and “Granny Lastname” to the other set.
In norwegian, an alternative to mormor/farmor is “Bestemor” (Best Mother. I don’t know why) with the shortened form being “Besta”. Since the norwegian word “best” is identical in meaning to the english one, I thought you might like it.
Granna
Grappa
My parents drink too much wine
I called my grandmothers “Grandmother” and “Granny.” My MIL is called “Nanna” by her grandkids, and my mother is called GeeGee (with a hard G.) My husband’s grandmothers are Granny (lastname), both of them.
I call them grandma and grandpa. But they don’t answer because they are dead.
I called my own grandmothers Grammy and Grandma [Last name].
My mother and I cooked up “Grandmother” for her … is sounds nice and dignified and once the kids are used to it, it doesn’t sound so formal. My 4-year-old has started saying Grammymother, which charms us all, so that’s what she’ll probably stay.
Other side is Grandma and Grandad
My grandmothers were “Mom Mom” (pronounced “Mum mum”) and “Nana.”
I recently had my first child. My sister and my wife’s sister had kids before us, so the grandmother titles were already pretty well-established. My mom is “Gigi,” which has always been her nickname. My wife’s mom is “Grammy.”
Hey, ignorance fought! There’s an older Greek woman in our neighborhood who everyone calls Ya-ya, and I never knew why!
To answer the OP, some of the grandmotherly names around our family:
Grandma
Nonnie
Granny
Grammie
and my favorite - Big Mama (my grandmother’s grandmother)
My mother’s mother is “Momma”. My father’s mother is “Nana”. My father’s father is “Grandpa”. My mother’s father died before I was born. My grandpa’s second wife I call by her name “Terry” and my stepdad’s mom I called by her name “Dorothy”. Stepdad’s dad also died before I was born. I’ll sometimes refer to any of the females as “my grandmother” or “my grandma” to people who wouldn’t know who the “pet names” referred to. I call my mom “Mom” and my dad “Dad” though I called him “Papa” when I was littler.
My mother called both her grandmothers Grandma.
When I was born my grandmother declared that only old ladies were Grandma and she would be known as Nana.
When my son was born my mother declared that only old ladies were Nana and she would be known as Grandma.
Have your grandchild call you what ever makes you happy, just realise will be a very special relationship.
My family uses Baba as well (the whole extended family!) One of my cousins actually used Grandma, and we all think she’s a freak because of it.
I’m Ukrainian, so it came from that language. Well, I mean, my ancestry is Ukrainian, not that I am actually from the Ukraine. You know what I mean.
The only grandparent I knew personally and lived with was Grandma. No other title was ever mentioned.
Nanny and Papa across the board and when I was born I had at least 10 living grands and great grands that I recall off the top of my head - including two great-great grandmothers. One of my great-great grands I called Nanny Mac and the rest usually by Nanny “first-name”. (Nanny Mac was a McDonald) Only one step-grandparent was called only by her first name. I think my mom and siblings didn’t much care for her and so she was simply “first-name” to all the cousins, too.
My mother called her grandparents Nanny and Granddaddy. I don’t know why my generation changed his name to Papa. My kids, 2 being half German, all refer to their paternal grandparents as Oma and Opa.
It wasn’t confusing at all to call them all one set of names. I think each family just finds something that fits their style and relationship.
My maternal grandparents: Grandmother and Papa
My paternal grandparents: MawMaw and PawPaw
My children call my in-laws Nana and PawPaw, and my parents Granny and Granddaddy.
Aside: My husband is the eldest grandchild in his mom’s family, and he named his grandmother “Gammaw”, because he couldn’t pronounce Grandma, and so now all the grandchildren call her that. Except for our 3 year old, who can say Grandma and refuses to call her anything else!