I married my husband and all the grandchildren were born after. We are a big blended family. They all have a nana, gma etc, they all have 3+ grandads with name inserted.
Now I am a huge part of grandchildrens lives and in reality I am the biggest caregiver to them all after their parents. They are all under 12. I organise all birthday parties, I organise taking them on holidays with DH and I, I take them to clubs, I'm at all school events and all activities, they all have their own room setup and 2 of them practically live here at weekends and school holidays. Just because biologically I'm not related doesn't make me any less their family or vice versa. They are all accounted for in my personal will and I have trusts set up for each of them. Me not DH.
However I am neither nana or gma or grandma. I'm me, MilkMilk, I started that, it's what I wanted to be known as, my sc have asked me on several occasions if I want to change, no im MilkMilk. I always have been and always will be. So much so that DH, dsc, friends and family all refer to me as this. I'm on all school contact forms as MilkMilk (Grandad Trays wife).
Often when out with dc I will introduce myself to adults as MilkMilk and then follow up with "nana" in air qoutes. I shouldn't have to explain my relationship but it comes up often. I hate being referred to as grandads wife except on forms as I feel this devalues me and what I do within the family. But equally I don't need to be "nana" etc. I love my name and the love I feel when the dc say it.
I understand your feelings op and I agree if your not comfortable with her having the "nana" tag then that's fine. That as a parent is your choice. But equally she is desperately trying to be apart of yours and dc life. She is proud of her role and clearly sees herself as "nana". Please don't devalue that. Don't come between that because of a title.
Just explain to her that she is very much a huge part of dc life and will always have that role, but the title is reserved for your mum. Ask her what she would like to be known as, suggest a pet name that dc can use forever. It won't her hurt her feelings and if you explain properly she will understand but if you just go in saying no, your not "nana" it will hurt her so much. She will be more than your fathers wife to your dc and and she clearly feels more than that to. Find a compromise with her and let her know that she is valued.