CrochetJo, I understand how you feel. Becoming a grandparent for the first time is exciting, and also a very emotional time, and many of us do like to decide on what we would like to be called by our grandchild. Whatever name you eventually choose, your grandchild will no doubt come up with their own version of it, but it'll be special to you!
I also understand why you may feel a little upset at not being referred to by a particular name, whether it's one you have chosen yourself, or one that your daughter has chosen for you (for now), especially when all of the GPs have their names.
Emotions are obviously running high in your household right now, and your daughter's hormones will be all over the place. Maybe the name you chose simply reminds her of what she called her own GM, who you say she didn't have much of a relationship with. Just give her time, and continue to be the supportive, caring mum that you seem to be. When things settle, and your daughter is in a good mood, I'd just start a light-hearted conversation with her, and ask her, isn't it about time you had a name that you can be referred to as a grandparent? If she really is against 'Nanny', I'm sure you can come up with something else between you ... NanJo, GranJo, GanJo ...? I wouldn't get too worked up about whatever name is chosen, because your lovely little grandchild will eventually choose whatever he/she decides once they begin to talk!
Congratulations on becoming a grandparent, and don't let this little issue spoil what is such a special time for you all!
I've got another 'keen'... Ouch!