Traditional grandparent names vs varient

My brother and I grew up calling our grandparents "Grandma and Grandpa." Mostly because my dad is a traditionalist on that and if you call them anything else, it's stupid and weird.

My cousins on my dad's side call them "Mema or Memes" and "Papa."

My dad nearly had a breakdown every time he heard them called that for a few years before just tolerating it.

Now I am pregnant and like the idea of my child calling my mom "Nana" instead of grandma. My mom looks nothing like a grandma. Not that she looks too young or anything, she looks the right age, but just not like, you know, a grandma. I honestly think nana is cuter and would suit her better. My mil already has 3 grandchildren and looks younger than my mom (even though she is older), but all the grandkids call her grandma and it honestly suits her. I just know if I bring it up to my parents, my dad would start saying how weird it is and openly cringe every time. My mom, on the other hand, would probably be more understanding.

Should I just go with "grandma"? Or should I try to get them to see my side of it?

Btw, my dads parents love what my cousins call them, it's only my dad who has a problem. He even had a problem with other grandchildren we aren't related to calling their grandma "Oma"! Which is GERMAN FOR GRANDMA.

Edit: I feel like I should tell the story of why my cousins call my dad's mom "Mema."

According to grandma, the story goes like this; my older cousin was 3 years old and came out of the house looking for his mom. (My dad's sister, so, my aunt.) She was at work and he was staying with grandma.

"Mommy!" He called, seeing grandma.

"I'm not mommy, I'm grandma." Grandma said, sitting on her porch.

Cousin looked confused, and said "mommy." The stubborn 3 yr old he was.

"Again, grandma!" Grandma corrected.

"MEMA!" Cousin then said with all the sterness a 3 yr old could muster.

"What?" Grandma laughed.

"Mema. Mommy, mema, mema, mommy." Cousin said. The name stuck. So now he, his brother, and little sister all call her Mema.

In my dad's eyes, Cousin should have been corrected more firmly and the "mema" fiasco should have been shut down.

We don't know where "Papa" came from, I think that's what my aunt wanted her kids to call grandpa, and he liked it. I like it too, but my dad firmly likes Grandpa or Grampa. I find "grampa" weird. So it shall be "grandpa".