Your question about Grandma's memory loss, and forgetting her granddaughter's name very clearly points out that Alzheimer's disease is a family challenge. How to help your 10-year old daughter deal
with what she feels is a "slight" due to Grandma's illness is a challenge that you can help her overcome.
No matter your age, learning that a loved one has Alzheimer's dementia can be devastating, and children and younger people seem to be more severely impacted by the changes in the patient.
As a parent, it's often difficult to know how much to explain to your children, and your desire to protect your children is a natural reaction in stressful times. However, one of the most important things you can do is to explain to your daughter, at an age appropriate level, exactly what is happening with Grandma.
By telling your daughter that Grandma is sick, just like when your daughter had the measles or chicken pox etc. In this case, Grandma's illness affects her memory, so instead of having red dots or sniffles, Grandma forgets things, even important things like names, but that doesn't mean that she doesn't love her granddaughter.
In fact, this is a great opportunity for the granddaughter to be a "big girl" and help Grandma remember. Suggest that your daughter show Grandma photos of the two of them, and recount the stories of things they did together in better times. Doing this not only helps build a memory bridge, even if only for a few minutes, between Grandma and granddaughter, but gives your daughter a role to play in helping Grandma. Her efforts may bring a smile to Grandma's face, and for just that moment, may bring recognition and recall of her name by simply having your daughter saying things like, "Remember this, when you and I, Julie, went to the beach?" Those techniques work.
However, the first thing I suggest is to help your daughter understand the problem that Grandma is facing, and be certain to assure your daughter that Grandma's forgetfulness is not directed at her granddaughter, but is part of the illness. That should provide some reassurance and relief for your daughter.
Your being open and honest is crucial because it is an opportunity to build trust with your daughter, even when dealing with matters that may be unpleasant or sad. But doing so will teach your daughter that she can trust you, and that she'll always have your support as a parent, even when times are emotionally difficult.
Also, be aware that your daughter will watch, listen and learn coping skills from you as she observes how you deal with distressing situations. The coping skills she learns from you will become part of who she is as she grows into adulthood and faces adversity as a natural part of her life. This is a compassionate teaching opportunity that will become a lifelong lesson, so how you approach it matters.
The most important aspect to remember is to be as honest with your daughter as you can be, based on her age and how much she can emotionally handle at this time. You may have to adapt some of the things you say, but be sure that your daughter knows that she is allowed and encouraged to ask questions and share her feelings with you without facing a judgmental response. Your daughter has to know that you still love her, and that whatever happens with Grandma, it's not her fault, and that deep down, Grandma still loves her, even if she can no longer clearly convey that message by name or statement.
Be sure to give your daughter plenty of reassurance and hugs, and don't be afraid to use humor as it frequently helps if you can laugh about the situation together.