Does my grandfather have the right to have his personal care by the nurse he wants?

Of course he has the right to want his favorite caregiver.
If it is a good caregiver I am afraid he will have to get in line. None of us can usually get the exact thing one wants. 97 or any other age does not change facts.

Of course he should be able to have his favourite caregiver, but it is sometimes not that simple. Whether this person is coming into his home or he is in a facility there will be scheduling considerations and of course the needs/desires of caregiver herself.

Serenity. Your message was cut off. Check it so we can see what you intended to ask.