I am writing an article on Fermat's work in number theory and feel uncomfortable everytime I have to write "Fermat's Little Theorem": it's clumsy and belittles the fundamental character of Fermat's result. "Fermat's Theorem" is too ambiguous, and I don't really like acronyms such as Flt or Flit. Has anyone ever seen a better name for this result (or a new suggestion)?
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.
Compared to Fermat's two squares theorem, or Fermat's four squares theorem, Fermat's Little theorem is indeed Little.
Not to mention the hard-to-prove Fermat Last Theorem, which goes under FLT; so that acronym, or a contraction Flt isn't suitable as it will cause confusion.
Therefore one might as well stick with "Fermat's Little Theorem" itself. I have given above a reasoning that it is comparatively little.
Der kleine Fermatsche Satz? This is how it started.
Fermat's congruence. This would be in line with Kummer's congruence, or Clausen-von-Staudt congruence etc.
The success of this name is foreseeable.
I agree with Gjergji Zaimi's comment above: Both "Fermat test" and "Fermat primality test" are short and descriptive.