Some are prouder of the title than others

Rico says that would be 'grandmother', as Alexandra Zissu discusses in an article in The New York Times:

Last month, Gwyneth Paltrow, promoting her new cookbook, My Father’s Daughter on the television show Chelsea Lately, revealed that her mother, the actress Blythe Danner, wanted to be called Woof by her grandchildren, Apple and Moses. “My mom’s hot, and she didn’t want to be called Grandma,” Ms. Paltrow said. “So she kept trying to make the Woof thing stick. It’s even her email address.”
Ms. Paltrow did not elaborate on the provenance of Woof, nor on her children’s actual nickname for Ms. Danner: Lalo. But another Hollywood grandmother, the actress Goldie Hawn, has written about her own reluctance to embrace the term in her best-selling memoir, A Lotus Grows in the Mud: “The wonderful day arrived; my grandson, Ryder Russell, burst forth into this world. I could barely contain myself. But was I really a ‘grandmother’?” Ms. Hawn wrote. (Or, as Shirley MacLaine howled in the 1983 movie Terms of Endearment: “Why should I be happy about being a grandmother?”) It is, Ms. Hawn continued, a “word that had so many connotations of old age and decrepitude. My son Oliver decided I should be called ‘Glam-Ma,’ which I thought was quite brilliant and made us all laugh so hard.”
The term has stuck. According to UrbanDictionary.com: “If sixty is the new forty, then GlamMa is the new Grandma, a woman with a sense of self and style.”
Resistant to being called anything that makes them sound old, baby-boomer grandparents have taken to accepting toddlers’ neologisms and ethnic variations or, better yet, naming themselves.
Mickey Sauls, 28, a sales coordinator for Ralph Lauren who lives in San Diego, is due to have her first baby in early June. Her parents’ names are already picked out. “My mother initiated the conversation,” Ms. Sauls said. “She has since changed her mind a few times.” For now the new grandmother, Irene Dawson, will be known as Nonna, a nod to her Maltese heritage. Initially Ms. Sauls’s father, John Dawson, wanted to be called by his first name, but he has now settled on Papa John (when he discovered the pizza chain Papa John’s recently, he texted his daughter a photo of “his personal logo”). “My wife and I were somewhat serious about being called Irene and John,” Mr. Dawson said. “We like our names and that it’s real. Grandpa, Grandma, Granny, Nanna, Gramps, etc., give off a vision of being old.”
This is a common attitude, said Dana Points, the editor-in-chief of Parents magazine. “Today’s grandparents don’t feel like they look or act like the grandparents of a generation ago,” she said, “so there can be a weird disconnect with the official term.”
Grandparents seeking help finding just the right appellation can choose from trendy, playful, international or traditional options at Grandparents.com. They can also turn to The New Grandparents Name Book, a Lighthearted Guide to Picking the Perfect Grandparent Name. Written by the mother and daughter team Lin Wellford, 59, and Skye Pifer, 35, it offers seven hundred unstodgy options, like G-mom, Doodad, Popsi, Bubba, and “Sonoma and Napa for a more sophisticated set.”
As someone “fun” and “still wearing jeans,” Ms. Wellford herself settled on “Mimi”. “It turns out most baby boomers I know felt the same way— love the idea, hate the name; we are such a herd,” she said. And Ms. Pifer approved. “She’s super-creative,” she said of her mother.
Freestyle naming has advantages in the modern world of divorced or otherwise fractured families. “Lots of kids have more than two sets of grandparents, so one reason to choose other names is to better distinguish them from one another,” Ms. Points said. Names can “defuse a situation that could be tense,” Ms. Wellford said. “No one wants to move in on grandmothering territory.”
Anna Crafton Walker, 36, a learning specialist who lives in Brooklyn, had four sets of grandparents to name, “no easy task,” she said. Her mom is now “Mamo”, which incorporates the nickname Mo, an abbreviation for Mother Crafton. Her dad is PawPaw, which he chose because it reminded him of his Kentucky grandfather, PooPoo, and the pawpaw tree he had growing in his backyard. Ms. Walker’s son, Wyatt, 2, also has a Nana, a Buya Buya, a PopPop, a Q, a Nonna, and a Grandma Patty. (Phew.)
Note to grandparents: if your grandchild wants to rename you (Ms. Danner told Babycenter.com that it was young Apple who came up with Lalo), “you have to be kind of relaxed about it,” Ms. Wellford said. “Seeing yourself as a GlamMa helps you make that leap into grandparenting, through that psychic distance between ‘I’m too young’ and ‘Wow, I love this grandchild, what a great idea.’ ”

Rico's ladyfriend, with only one grandchild so far, is more than happy to be called 'grandma'. Rico says he would be happy with 'Bubba' (but not PawPaw; that was his cousins name for his grandfather Wilson), but we'll just wait and see what the kid comes up with on her own...