I think you shouldn't change the name. It's universally known as Fermat's Little Theorem, and especially if you're writing a survey or historical article, you're not in a place to try to revolutionize established mathematical nomenclature. There are many instances of unfortunate terminology in mathematics, but in my opinion, once they are in general use, they become part of the lore and the culture. I would make exceptions only in a few cases, such as:

a) it's on the level of adjectives such as "good" and "admissible", b) it's crediting the wrong person (Cayley numbers, Burnside's lemma), or c) it's very recent, with the inventor implicitly begging to attach his name to it

And if your life work is going to become known as "Lemmermeyer's dirty trick", well, take it with humor.