My experiences with this difficulty come from two things; my experience working in a nursing home and our experiences with our elders in assisted living. This article will be more about how to choose a gift than what gift to give. And you can also discover the best gifts for dementia patients at https://gleaminyoureye.com/.
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Space: Unless the person is in a private room there are going to be space issues. Even a two-bedroom will have some of this difficulty. An example we've had to cope with is our elder's television set. It was a gift, and it may turn out to be a problem. You see, it's a 60 inch set and not all single rooms are set up for something that size.
On the Ward: Hospitals, nursing homes and some skilled care facilities have wards as well as rooms. In a ward there can be a dozen people. Not only is there a big space issue there is a "people" issue. What if someone in the ward doesn't like it? What if they like it enough to "borrow" it? What if someone is jealous? These issues are even worse if the ward is part of a dementia unit.
Rules: All facilities have rules about what a patient can have. Assisted living is pretty lenient until you get to the memory care unit. The rules in that unit have to be strict for everyone's safety. As an example here we've had to remove every pair of scissors our elder had and we have to keep an eye out that she doesn't slip into an office and "borrow" the director's.
There are also things that people with medical conditions can't eat. Bringing a diabetic a pound of chocolate candy isn't wise. Talk to your elder's doctor about food and other restrictions before selecting a gift.