I was discussing with some friends about synonyms when we found, that ironically nobody of us knew any synonyms to the word "synonym" itself. Are there any?
A thesaurus gives analogue as the definition for synonym and equivalent and metonym as synonyms.
synonym for synonym is equivalent term
The synonym of synonym is "poecilonym"
I think that you could only find an antonym, which is, in fact, 'Antonym'... 'Equal' 'The Same' 'Exact' 'Similar' or 'Equivalent' are some words and phrases that could be used, however I can't provide you with a perfect answer.
I would disagree: Greek poikilos means varied, diverse, not "same". Poicilonymy is the use of different words to refer to the same thing, in literary texts usually known as 'elegant variation'.
A metonym is an associated term used as a substitute for 'the real thing': 'reports from number 10' for 'reports from the Prime Minister's Office'. Paronym would be the neatest but, along with heteronym, it has been made a term of linguistics for specific types of (near) synonyms or equivalents, but how technical do you want to get?
It's surprising, given how much it was hammered into us at school 50 years ago that there were few exact synonyms, that there isn't a term for words with near-identical meanings. Lancelot Hogben in The Mother Tongue, 1964 (read it, everyone) uses/invents paranym, which I haven't been able to find in a dictionary but is, I think, the nearest to what we're looking for, or at least a useful word. He defines it (P276) as: words that share a common meaning but have widely different alternative meanings, eg but/yet:
BUT: 1. YET; 2. except.
YET: 1. TILL NOW/THEN; 2. but.
What about homeonym? If we concentrate on meaning rather than name, then we could have homeosemy alongside polysemy.
A quick Google search of define synonym brought the following synonyms:
alternate, substitute, alternative, equivalent, euphemism
Wikitionary and Sunil Raina suggest
metonym as a synonym for synonym.
Equivalent term (or word) is suggested by Synonymy.
homonym as a third choice.
Proxy just might not reflect the main idea...