I don't know if this will help at all, but I'd just be thankful that she knows who you are, because so many people with degenerative illnesses like alzheimers and dementia forget who people are, and who they are. They start calling you by your fathers name, or their husband etc because they forget the recent things but can remember the old stuff in their memory. I don't know exactly what your grandmother has, but just be thankful that she's around and knows who you are, even if she doesn't address you the right way. I think my grandfather is starting to loose his mental capacity a little, but unfortunately I've cut him out a lot because he's full of homophobic and racist beliefs (he turns the tv off if there's a gay couple on and is constantly complaining that foreign people are on his tv and should go back to heir own channels). I wish I could stomach him more because he practically brought me up, and I might not have so long left with him, but I can't.
Everyone calls me by female pronouns because I'm not out, and the way I deal with it is remembering that they know the real me, I'm not putting on an act or anything, but they just put a different label on me. Everything they know is right, but they make a little mistake when referring to me, so it's not such a big deal. That's how I can cope with my girlfriend thinking I'm a lesbian, she knows the real me, but just sticks an 's' in front of 'he' when thinking about me. It's not deliberate, she just doesn't know, but she does know the real me still. I'm not sure if that makes sense or is helpful, but it's just how iI think about things.