What is a noun for synonym?

There isn't a single perfect noun for "synonym." However, depending on the context, you could use:

General terms:

* Equivalent

* Parallel

* Substitute

* Counterpart

* Correspondence

More specific terms:

* Lexical equivalent (emphasizing the language aspect)

* Near-synonym (for words with similar but not identical meanings)

* Thesaurus entry (referring to a list of synonyms)

The best option will depend on what you're trying to say.