How can we help my grandmother when she keeps saying that her room is not her room even though everything is there?

The sad thing is that this can happen to people who are still in their own homes, they begin to look for a home from a different time or place, perhaps their childhood home. You will probably never get very far if you are trying to convince her that the room is hers, and over time she may begin to distrust you. Try instead to point out that this is a nice place; mention the food, the friends, the staff who take good care of her etc. You might point out how cozy her room is, just like her one at home! When she wants to go home have a plausible reason why you can't go today... there is road construction or the car need to go to the shop, or perhaps tell her that she can go home when the doctor says it's OK. Validate and redirect.