I grew up in a situation like this where my mom was still getting use to having a new "step-mom". She wasn't happy about it and didn't like Jennie at all. Because of her feelings, she raised us kids to call her by her name (Jennie). It felt normal for me for a while until I realized how much it might have hurt Jennie's feelings, regardless of how my mother felt about the situation. I think it would have been more fair for us kids to come up with a name.
When I was about 10 or 11, one day, I asked Jennie if she would prefer being called Grandma and she said it was up to me. ( I could tell she was so happy that I had even asked her that.) But because I had been raised to call her by her name, it felt too weird to suddenly start calling her something else. But I call her Nana Jennie and that works really well for us both. My mom has a changed heart about it and feels a little guilty for not including her more as a "grandma" even if she isn't one by blood. Jennie is now the closest thing left to a grandparent that I have (all four of my blood grandparents passed away 2 years ago) and I'm very grateful to have her as such.
I just think it's worth thinking about a little more. I think it's super weird and totally out of line for Linda to assume anything being as she's not even been around long enough to fill that roll for you or your LO....but maybe give it some time, don't worry about it so much now, and you may feel differently later. If not, and if nothing else, I really recommend letting your LO find a name for her.