This article describes a concept which is mentioned in J.R.R. Tolkien's works, but was never given a definite name.
In published writing referring to the early legendarium, only the term Old Noldorin was used. In that early conception, it was the language spoken by the Gnomes in Kôr, (in contrast to the later legendarium, where the Noldor spoke Quenya both in Valinor and later in Middle-earth). Old Noldorin does show some similarities to Quenya and Telerin.
Most of the corpus of ON is given in The Etymologies and their purpose is to illustrate the etymology of some Noldorin words. Even after Tolkien renamed "Noldorin" into "Sindarin", the same rules of etymology and derivation have been retained. It is therefore possible that an ancient form of Sindarin similar to what Tolkien imagined as "Old Noldorin" did exist in the First Age of his later concepts.
More recent works like Quendi and Eldar show ancient forms of Sindarin that seem to possess the same structure and to belong to the same evolution as the Old Noldorin of the Etymologies; but Tolkien did not give a name to that stage of language, making "Old Sindarin" to seem a non-canon, but plausible name for it.
Note that in these recent sources, Tolkien provides these forms with an asterisk as "unattested", suggesting that they belong to an unwritten stage of the language. This is not the case in the "Old Noldorin" forms of the Etymologies where they are unasterisked.