I’m writing a senior reflection paper and I refer to my grandmother as nanny just as she called her grandmother. However I’m wondering if that is too informal for an essay. Also maybe a little confusing because the U.S meaning is like a long term caregiver.
In the U.S., a nanny cares for children in employ of the parents.
I think that the question is not whether nanny is too informal for an essay, but is the term clear to your target audience. If you think won’t be then you have two solutions: the first is to not use the word nanny for your grandmother and the second is to explain the term, either explicitly or by context.
Explicitly is clear enough but might not fit with the style of the writing or tone of the piece — lacking intimacy and affection.
To make clear the term by context, use it in a sentence that links to two phrases: My grandmother Broomhilde Groom, darling nanny, lives on in my memories. Or some sort of similar statement that shows that nanny or nan are terms you use to refer to your grandmother. Then stick to one term for the remainder of the piece.