* If you're looking for a word that means the *exact* same thing: There isn't really one. "Synonym" is already a very specific word.
* If you're looking for words that are similar in meaning: You could use words like equivalence, parallel, analog, or counterpart.
* If you're looking for a word that describes the *concept* of synonymy: You could use equivalency, interchangeability, parallelism, or correspondence.
So, the answer really depends on the context and what you're trying to convey!